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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.

Respuesta :

kudzordzifrancis

Answer:

7

Step-by-step explanation:

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

[tex]\lim_{x \to 0^-} f(x)=7-x^2[/tex]

[tex]\lim_{x \to 0^-} f(x)=7-(0)^2=7[/tex]

The right hand limit is

[tex]\lim_{x \to 0^+} f(x)=10x+7[/tex]

[tex]\lim_{x \to 0^+} f(x)=10(0)+7=7[/tex]

Since the left hand limit equals the right hand limit;

[tex]\lim_{x \to 0} f(x)=7[/tex]

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