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# The limit of a symbolic expression

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Simon K on 27 Feb 2021
Answered: Walter Roberson on 27 Feb 2021
The limit of fp which is defined below is piecewise(k == 0, 0), but I am not sure what this means. k is some constant, and the limit should be k times the limit as s approaches of (s+5)/(s*(s+6)*(s+7)*(s+8) or infinity.
syms s k
fp = k*(s+5)/(s*(s+6)*(s+7)*(s+8));
limit(fp,s,0)
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### Answers (1)

Walter Roberson on 27 Feb 2021
The limit of constant 0 times f(x) is 0 unless f(x) approaches infinity at the same rate that the constant 0 approaches being 0. Which is to say that if f(x) is the constant infinity or negative infinity, then yes 0*f(x) would be undefined. But your function approaches infinity more slowly than 0 constant approaches being 0, so 0 times the s ratio has a limit of 0. Therefore you need to special-case k=0 .
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