The limit of a symbolic expression

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) 

Answer 1

[Walter Roberson]

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 .