Question

Find the indicated limit, if it exists.(7 points)

limit of f of x as x approaches 0 where f of x equals 7 minus x squared when x is less than 0, 7 when x equals 0, and 10 x plus 7 when x is greater than 0

Choices below

3

10

7

The limit does not exist.

Answer 1

7

Explanation:

The left hand limit is when we approach zero from left. We use the function on this domain in finding the limit.

`\lim_(x \to 0^-) f(x)=7-x^2`

`\lim_(x \to 0^-) f(x)=7-(0)^2=7`

The right hand limit is

`\lim_(x \to 0^+) f(x)=10x+7`

`\lim_(x \to 0^+) f(x)=10(0)+7=7`

Since the left hand limit equals the right hand limit;

`\lim_(x \to 0) f(x)=7`