Problem

Example equation: g(h(x)) lim x -> -1

When the h(x) for the lim of x -> -1 doesn’t exist people wonder what to do but there’s a way to solve these kind of problems

Look at the limit from left and right sides

lim x -> -1 & lim x -> -1

Now solve the problem with using those limit definitions

Solution

lim g(h(x)) = lim g(h(x)) = 3 x -> -1 h(x) -> -2

lim g(h(x)) = lim g(h(x)) = 3 x -> -1 h(x) -> -3

You also have to check where the limit is approaching from greater or smaller numbers as that also indicates the + and - sign on the numbers