Question

Find the limit , picture provided

Answer 1

d. does not exist

Explanation:

The given limits are;

`\lim_(x \to 4) f(x) =5`,
`\lim_(x \to 4) g(x) =0` and
`\lim_(x \to 4) h(x) =-2`

We want to find

`\lim_(x \to 4) (f)/(g)(x)= \lim_(x \to 4) (f(x))/(g(x))`

By the properties of limits, we have;

`\lim_(x \to 4) (f)/(g)(x)= (\lim_(x \to 4) f(x))/(\lim_(x \to 4) g(x))`

This gives us;

`\lim_(x \to 4) (f)/(g)(x)= (5)/(0)`

Division by zero is not possible. Therefore the limit does not exist.