Find lim_(x rarr-5)((x+1)^(2))/(8-x). Choose 1 answer: (A) (16)/(13) (B) 2 (C) 12 (D) The limit doesn't exist

Check Validity of Substitution: To find the limit of the function (x+1)²/(8-x) as x approaches -5, we can directly substitute the value of x with -5, as long as the substitution does not result in a division by zero or an indeterminate form.Substitute x with -5: Substitute x with -5 into the function (x+1)²/(8-x). (((-5)+1)²)/(8-(-5)) = (4)²/(8+5) = 16/13.Verify Valid Numerical Value: Since the substitution resulted in a valid numerical value and did not cause any indeterminate form or division by zero, the limit exists and is equal to the calculated value.Final Answer: The final answer is 16/13, which corresponds to option (A).

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Find $\lim_{x \to -5}\left(\frac{(x+1)^{2}}{8-x}\right)$ . $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{16}{13}$ $\newline$ (B) $2$ $\newline$ (C) $12$ $\newline$ (D) The limit doesn't exist

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Math Problems

Algebra 2

Sum of finite series starts from 1

Full solution

Q. Find

\lim_{x \to -5}\left(\frac{(x+1)^{2}}{8-x}\right)

\newline

Choose

1

answer:

\newline

(A)

\frac{16}{13}

\newline

(B)

2

\newline

(C)

12

\newline

(D) The limit doesn't exist

Check Validity of Substitution: To find the limit of the function $(x+1)^2/(8-x)$ as $x$ approaches $-5$ , we can directly substitute the value of $x$ with $-5$ , as long as the substitution does not result in a division by zero or an indeterminate form.
Substitute $x$ with $-5$ : Substitute $x$ with $-5$ into the function $\frac{(x+1)^2}{8-x}$ . $\frac{((-5)+1)^2}{8-(-5)} = \frac{(4)^2}{8+5} = \frac{16}{13}$ .
Verify Valid Numerical Value: Since the substitution resulted in a valid numerical value and did not cause any indeterminate form or division by zero, the limit exists and is equal to the calculated value.
Final Answer: The final answer is $\frac{16}{13}$ , which corresponds to option (A).