Question

Find lim f(x) if f(x) x->5 = { -x² -1, x #5 -3, x=5

Answer 1

Given

$f(x) = \begin{cases} -x^2 - 1 & \text{if }x \neq 5 \\ -3 & \text{if }x=5 \end{cases}$

we have

$\displaystyle \lim_{x\to5} f(x) = \lim_{x\to5} (-x^2-1) = -5^2-1 = \boxed{-26}$

since we are approaching $x=5$, so effectively $x\neq 5$ and we use the definition of $f(x)$ under that condition.