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Find
lim_(x rarr-1)(x^(2)-9)/(x^(2)+1).
Choose 1 answer:
(A) -4
(B) -5
(c) -9
(D) The limit doesn't exist

Find $\lim _{x \rightarrow-1} \frac{x^{2}-9}{x^{2}+1}$ . $\newline$ Choose $1$ answer: $\newline$ (A) $-4$ $\newline$ (B) $-5$ $\newline$ (C) $-9$ $\newline$ (D) The limit doesn't exist

View step-by-step help

View step-by-step help

Evaluate an exponential function

Full solution

Q. Find

\lim _{x \rightarrow-1} \frac{x^{2}-9}{x^{2}+1}

.

\newline

Choose

1

answer:

\newline

(A)

-4

\newline

(B)

-5

\newline

(C)

-9

\newline

(D) The limit doesn't exist

Identify the function and point: Identify the function and the point at which we need to find the limit. The function given is $(x^2 - 9)/(x^2 + 1)$ , and we need to find the limit as $x$ approaches $-1$ .
Substitute value into function: Substitute the value of $x$ into the function to see if the function is defined at that point. $\lim_{x \to -1}\frac{x^2 - 9}{x^2 + 1} = \frac{(-1)^2 - 9}{(-1)^2 + 1}$
Perform the calculations: Perform the calculations. $\newline$ $((-1)^2 - 9)/((-1)^2 + 1) = (1 - 9)/(1 + 1) = (-8)/2 = -4$
Conclude the limit: Conclude the limit. $\newline$ Since we were able to directly substitute $x = -1$ into the function and get a real number result, the limit exists and is equal to $-4$ .

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