Question

How do you find the limit of `2x+5` as `x->-7`?

Answer 1

Please see below.

Explanation:

When `x` is very close to `-7`,

`2x` is very close to `2(-7) = -14`,

so `2x+5` is very close to `-14+5 = -9`.

The limit is `-9`.

In the end, we get the same number as we get by substitution `-7` for `x`.

For some functions, we do not get the same result by substitution. So it is helpful to understand the slightly different reasoning for limit and substitution.