{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-06T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":44848,"title":"Approximate the inverse tangent by power series","description":"Given values b (where abs(b)\u003c=1) and n (polynomial order), write a function that calculates atan(b) by using power series. ","description_html":"\u003cp\u003eGiven values b (where abs(b)\u0026lt;=1) and n (polynomial order), write a function that calculates atan(b) by using power series.\u003c/p\u003e","function_template":"function y = myfun(b,n)\r\n  y = b+n;\r\nend","test_suite":"%%\r\nff = 'fileread';\r\nassert(nargin(ff)~=-1, 'empty file forbidden')\r\nfiletext = fileread('myfun.m');\r\nassert(isempty(strfind(filetext, '''')),'string forbidden')\r\nassert(isempty(strfind(filetext, 'varargin')),'varargin forbidden')\r\nassert(isempty(strfind(filetext, 'ans')),'ans forbidden')\r\nassert(isempty(strfind(filetext, 'atan')),'atan forbidden')\r\nassert(isempty(strfind(filetext, 'atan2')),'atan2 forbidden')\r\nassert(isempty(strfind(filetext, 'atand')),'atand forbidden')\r\nassert(isempty(strfind(filetext, 'atan2d')),'atan2d forbidden')\r\nassert(isempty(strfind(filetext, 'tan')),'tan forbidden')\r\nassert(~isempty(filetext),'empty file forbidden')\r\n%%\r\nb = 0.1;\r\nn = 3;\r\ny_correct = 0.09966667;\r\nassert(abs(myfun(b,n)-y_correct)\u003c1e-6)\r\n%%\r\nb = 0.01;\r\nn = 5;\r\ny_correct = 0.00999967;\r\nassert(abs(myfun(b,n)-y_correct)\u003c1e-6)\r\n%%\r\nb = 0.2;\r\nn = 3;\r\ny_correct = 0.19733333;\r\nassert(abs(myfun(b,n)-y_correct)\u003c1e-6)\r\n%%\r\nb = 0.2;\r\nn = 1;\r\ny_correct = 0.20000000;\r\nassert(abs(myfun(b,n)-y_correct)\u003c1e-6)\r\n%%\r\nb = 0.2;\r\nn = 7;\r\ny_correct = 0.19739550;\r\nassert(abs(myfun(b,n)-y_correct)\u003c1e-6)","published":true,"deleted":false,"likes_count":1,"comments_count":6,"created_by":274816,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":"2019-07-16T15:54:20.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-02-13T20:58:53.000Z","updated_at":"2026-03-16T12:37:21.000Z","published_at":"2019-02-13T20:58:53.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven values b (where abs(b)\u0026lt;=1) and n (polynomial order), write a function that calculates atan(b) by using power series.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":55775,"title":"Taylor Series","description":"You can use a Taylor series to approximate common functions. The Taylor series for sin(x) is \r\n\r\nUsing only the first several terms in the series could get you a good approximation to the function. \r\nWrite a function that takes a point x at which to evaluate the sine function and a tolerance level that defines how close you want the Taylor series approximation to be to the actual value. Your function should output the approximate value of sin(x).","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 157px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 78.5px; transform-origin: 407px 78.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eYou can use a Taylor series to approximate common functions. The Taylor series for sin(x) is \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 46px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 23px; text-align: left; transform-origin: 384px 23px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"294.5\" height=\"46\" style=\"width: 294.5px; height: 46px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eUsing only the first several terms in the series could get you a good approximation to the function. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes a point x at which to evaluate the sine function and a tolerance level that defines how close you want the Taylor series approximation to be to the actual value. Your function should output the approximate value of sin(x).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function yApp = myTaylor(x,tol)\r\n\r\n\r\nend","test_suite":"%%\r\nx = pi;\r\ntol = 0.01;\r\nyApp = myTaylor(x,tol); \r\nassert(abs(yApp-sin(x))\u003ctol)\r\n%%\r\nx = pi/2;\r\ntol = 0.1;\r\nyApp = myTaylor(x,tol); \r\nassert(abs(yApp-sin(x))\u003ctol)\r\n%%\r\nx = pi*1i;\r\ntol = 1e-3;\r\nyApp = myTaylor(x,tol); \r\nassert(abs(yApp-sin(x))\u003ctol)\r\n%%\r\nx = 2.345;\r\ntol = 1e-5;\r\nyApp = myTaylor(x,tol);\r\nassert( (abs(yApp-sin(x))\u003ctol) \u0026\u0026 (abs(yApp-sin(x))\u003etol/100) )\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":140016,"edited_by":140016,"edited_at":"2022-10-17T14:02:37.000Z","deleted_by":null,"deleted_at":null,"solvers_count":207,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-16T18:00:45.000Z","updated_at":"2026-04-02T08:59:19.000Z","published_at":"2022-10-17T14:02:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou can use a Taylor series to approximate common functions. The Taylor series for sin(x) is \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\sin(x) = \\\\sum_{n=0}^{\\\\infty}\\\\frac{(-1)^nx^{2n+1}}{(2n+1)!} = x - \\\\frac{x^3}{3!} + \\\\frac{x^5}{5!} - \\\\frac{x^7}{7!} + \\\\dots\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUsing only the first several terms in the series could get you a good approximation to the function. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes a point x at which to evaluate the sine function and a tolerance level that defines how close you want the Taylor series approximation to be to the actual value. Your function should output the approximate value of sin(x).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":44848,"title":"Approximate the inverse tangent by power series","description":"Given values b (where abs(b)\u003c=1) and n (polynomial order), write a function that calculates atan(b) by using power series. ","description_html":"\u003cp\u003eGiven values b (where abs(b)\u0026lt;=1) and n (polynomial order), write a function that calculates atan(b) by using power series.\u003c/p\u003e","function_template":"function y = myfun(b,n)\r\n  y = b+n;\r\nend","test_suite":"%%\r\nff = 'fileread';\r\nassert(nargin(ff)~=-1, 'empty file forbidden')\r\nfiletext = fileread('myfun.m');\r\nassert(isempty(strfind(filetext, '''')),'string forbidden')\r\nassert(isempty(strfind(filetext, 'varargin')),'varargin forbidden')\r\nassert(isempty(strfind(filetext, 'ans')),'ans forbidden')\r\nassert(isempty(strfind(filetext, 'atan')),'atan forbidden')\r\nassert(isempty(strfind(filetext, 'atan2')),'atan2 forbidden')\r\nassert(isempty(strfind(filetext, 'atand')),'atand forbidden')\r\nassert(isempty(strfind(filetext, 'atan2d')),'atan2d forbidden')\r\nassert(isempty(strfind(filetext, 'tan')),'tan forbidden')\r\nassert(~isempty(filetext),'empty file forbidden')\r\n%%\r\nb = 0.1;\r\nn = 3;\r\ny_correct = 0.09966667;\r\nassert(abs(myfun(b,n)-y_correct)\u003c1e-6)\r\n%%\r\nb = 0.01;\r\nn = 5;\r\ny_correct = 0.00999967;\r\nassert(abs(myfun(b,n)-y_correct)\u003c1e-6)\r\n%%\r\nb = 0.2;\r\nn = 3;\r\ny_correct = 0.19733333;\r\nassert(abs(myfun(b,n)-y_correct)\u003c1e-6)\r\n%%\r\nb = 0.2;\r\nn = 1;\r\ny_correct = 0.20000000;\r\nassert(abs(myfun(b,n)-y_correct)\u003c1e-6)\r\n%%\r\nb = 0.2;\r\nn = 7;\r\ny_correct = 0.19739550;\r\nassert(abs(myfun(b,n)-y_correct)\u003c1e-6)","published":true,"deleted":false,"likes_count":1,"comments_count":6,"created_by":274816,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":"2019-07-16T15:54:20.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-02-13T20:58:53.000Z","updated_at":"2026-03-16T12:37:21.000Z","published_at":"2019-02-13T20:58:53.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven values b (where abs(b)\u0026lt;=1) and n (polynomial order), write a function that calculates atan(b) by using power series.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":55775,"title":"Taylor Series","description":"You can use a Taylor series to approximate common functions. The Taylor series for sin(x) is \r\n\r\nUsing only the first several terms in the series could get you a good approximation to the function. \r\nWrite a function that takes a point x at which to evaluate the sine function and a tolerance level that defines how close you want the Taylor series approximation to be to the actual value. Your function should output the approximate value of sin(x).","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 157px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 78.5px; transform-origin: 407px 78.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eYou can use a Taylor series to approximate common functions. The Taylor series for sin(x) is \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 46px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 23px; text-align: left; transform-origin: 384px 23px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"294.5\" height=\"46\" style=\"width: 294.5px; height: 46px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eUsing only the first several terms in the series could get you a good approximation to the function. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes a point x at which to evaluate the sine function and a tolerance level that defines how close you want the Taylor series approximation to be to the actual value. Your function should output the approximate value of sin(x).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function yApp = myTaylor(x,tol)\r\n\r\n\r\nend","test_suite":"%%\r\nx = pi;\r\ntol = 0.01;\r\nyApp = myTaylor(x,tol); \r\nassert(abs(yApp-sin(x))\u003ctol)\r\n%%\r\nx = pi/2;\r\ntol = 0.1;\r\nyApp = myTaylor(x,tol); \r\nassert(abs(yApp-sin(x))\u003ctol)\r\n%%\r\nx = pi*1i;\r\ntol = 1e-3;\r\nyApp = myTaylor(x,tol); \r\nassert(abs(yApp-sin(x))\u003ctol)\r\n%%\r\nx = 2.345;\r\ntol = 1e-5;\r\nyApp = myTaylor(x,tol);\r\nassert( (abs(yApp-sin(x))\u003ctol) \u0026\u0026 (abs(yApp-sin(x))\u003etol/100) )\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":140016,"edited_by":140016,"edited_at":"2022-10-17T14:02:37.000Z","deleted_by":null,"deleted_at":null,"solvers_count":207,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-16T18:00:45.000Z","updated_at":"2026-04-02T08:59:19.000Z","published_at":"2022-10-17T14:02:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou can use a Taylor series to approximate common functions. The Taylor series for sin(x) is \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\sin(x) = \\\\sum_{n=0}^{\\\\infty}\\\\frac{(-1)^nx^{2n+1}}{(2n+1)!} = x - \\\\frac{x^3}{3!} + \\\\frac{x^5}{5!} - \\\\frac{x^7}{7!} + \\\\dots\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUsing only the first several terms in the series could get you a good approximation to the function. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes a point x at which to evaluate the sine function and a tolerance level that defines how close you want the Taylor series approximation to be to the actual value. Your function should output the approximate value of sin(x).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"term":"tag:\"taylor\"","current_player_id":null,"fields":[{"name":"page","type":"integer","callback":null,"default":1,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"per_page","type":"integer","callback":null,"default":50,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"sort","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"body","type":"text","callback":null,"default":"*:*","directive":null,"facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":false},{"name":"group","type":"string","callback":null,"default":null,"directive":"group","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"difficulty_rating_bin","type":"string","callback":null,"default":null,"directive":"difficulty_rating_bin","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"id","type":"integer","callback":null,"default":null,"directive":"id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"tag","type":"string","callback":null,"default":null,"directive":"tag","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"product","type":"string","callback":null,"default":null,"directive":"product","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_at","type":"timeframe","callback":{},"default":null,"directive":"created_at","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"profile_id","type":"integer","callback":null,"default":null,"directive":"author_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_by","type":"string","callback":null,"default":null,"directive":"author","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player_id","type":"integer","callback":null,"default":null,"directive":"solver_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player","type":"string","callback":null,"default":null,"directive":"solver","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"solvers_count","type":"integer","callback":null,"default":null,"directive":"solvers_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"comments_count","type":"integer","callback":null,"default":null,"directive":"comments_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"likes_count","type":"integer","callback":null,"default":null,"directive":"likes_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leader_id","type":"integer","callback":null,"default":null,"directive":"leader_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leading_solution","type":"integer","callback":null,"default":null,"directive":"leading_solution","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true}],"filters":[{"name":"asset_type","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":"\"cody:problem\"","prepend":true},{"name":"profile_id","type":"integer","callback":{},"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":"author_id","static":null,"prepend":true}],"query":{"params":{"per_page":50,"term":"tag:\"taylor\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"taylor\"","","\"","taylor","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007f2348271920\u003e":null,"#\u003cMathWorks::Search::Field:0x00007f2348271880\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007f2348270de0\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007f2348271ba0\u003e":1,"#\u003cMathWorks::Search::Field:0x00007f2348271b00\u003e":50,"#\u003cMathWorks::Search::Field:0x00007f2348271a60\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007f23482719c0\u003e":"tag:\"taylor\""},"user_query":{"#\u003cMathWorks::Search::Field:0x00007f23482719c0\u003e":"tag:\"taylor\""},"queried_facets":{}},"query_backend":{"connection":{"configuration":{"index_url":"http://index-op-v2/solr/","query_url":"http://search-op-v2/solr/","direct_access_index_urls":["http://index-op-v2/solr/"],"direct_access_query_urls":["http://search-op-v2/solr/"],"timeout":10,"vhost":"search","exchange":"search.topic","heartbeat":30,"pre_index_mode":false,"host":"rabbitmq-eks","port":5672,"username":"cody-search","password":"78X075ddcV44","virtual_host":"search","indexer":"amqp","http_logging":"true","core":"cody"},"query_connection":{"uri":"http://search-op-v2/solr/cody/","proxy":null,"connection":{"parallel_manager":null,"headers":{"User-Agent":"Faraday v1.0.1"},"params":{},"options":{"params_encoder":"Faraday::FlatParamsEncoder","proxy":null,"bind":null,"timeout":null,"open_timeout":null,"read_timeout":null,"write_timeout":null,"boundary":null,"oauth":null,"context":null,"on_data":null},"ssl":{"verify":true,"ca_file":null,"ca_path":null,"verify_mode":null,"cert_store":null,"client_cert":null,"client_key":null,"certificate":null,"private_key":null,"verify_depth":null,"version":null,"min_version":null,"max_version":null},"default_parallel_manager":null,"builder":{"adapter":{"name":"Faraday::Adapter::NetHttp","args":[],"block":null},"handlers":[{"name":"Faraday::Response::RaiseError","args":[],"block":null}],"app":{"app":{"ssl_cert_store":{"verify_callback":null,"error":null,"error_string":null,"chain":null,"time":null},"app":{},"connection_options":{},"config_block":null}}},"url_prefix":"http://search-op-v2/solr/cody/","manual_proxy":false,"proxy":null},"update_format":"RSolr::JSON::Generator","update_path":"update","options":{"url":"http://search-op-v2/solr/cody"}}},"query":{"params":{"per_page":50,"term":"tag:\"taylor\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"taylor\"","","\"","taylor","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007f2348271920\u003e":null,"#\u003cMathWorks::Search::Field:0x00007f2348271880\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007f2348270de0\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007f2348271ba0\u003e":1,"#\u003cMathWorks::Search::Field:0x00007f2348271b00\u003e":50,"#\u003cMathWorks::Search::Field:0x00007f2348271a60\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007f23482719c0\u003e":"tag:\"taylor\""},"user_query":{"#\u003cMathWorks::Search::Field:0x00007f23482719c0\u003e":"tag:\"taylor\""},"queried_facets":{}},"options":{"fields":["id","difficulty_rating"]},"join":" "},"results":[{"id":44848,"difficulty_rating":"easy"},{"id":55775,"difficulty_rating":"easy-medium"}]}}