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 \\eq 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\\eq 5` and we use the definition of
`f(x)` under that condition.