Question

limit, what can I do here?

Answer 1

Welp, if the limit approaches two different values from the left and the right, the limit doesn't exist. Poof.

Answer 2

do a one sided limit check

Answer 3

is it -1?

Answer 4

Cake for everyone.

Answer 5

I tried some values near -1

Answer 6

\(\bf lim_{x\to -1}\quad
\begin{cases}
cos(\pi x)&x<-1\\ \quad \\
\bf x^2-2& x\ge -1
\end{cases}
\\ \quad \\ \quad \\
lim_{x\to -1^-}\quad cos(\pi x)\implies cos(\pi \cdot -1)\implies cos(-\pi)
\\ \quad \\
\implies cos(\pi)\implies {\color{red}{ -1}}
\\ \quad \\
lim_{x\to -1^+}\quad x^2-2 \implies (-1)^2-2\implies 1-2\implies {\color{red}{ -1}}\)

Answer 7

alright, I thought I would need some algebra.. thanks!

Answer 8

yw