Question

What is the limit of `(t^2 - 3)^3(t + 3)^5` as t approaches -2?

Answer 1

`lim_(trarr-2)(t^2-3)^3(t+3)^5 = color(green)(1)`

Explanation:

As Eddie noted a couple months ago:

If `f(t)=(t^2-3)^3(t+3)^5`
since `f(t)` is defined at (and around) `t=-2`
`lim_(trarr-2)f(t) = f(-2)`
`color(white)("XXXXX")=((-2)^2-3)^3((-2)+3)^5`

`color(white)("XXXXX")=1^3 * 1^5`

`color(white)("XXXXX")=1`