Question

How do you find the limit of `(x^2+1)^3 (x+3)^5` as x approaches -1?

Answer 1

256

Explanation:

Since neither of the functions are undefined or indeterminate for x = -1 then the limit may be evaluated by `color(blue)"substitution"`

`rArrlim_(xto-1)(x^2+1)^3(x+3)^5`

`=lim_(xto-1)(x^2+1)^3xxlim_(xto-1)(x+3)^5`

`=2^3xx2^5=2^8=256`