Question

find the following limit or state that it does not exist.
\\(\lim \limits_{x \to -3} \frac{6x^2 + 7x + 11}{5x - 7}\\)

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

\\(\bigcirc\\) a. \\(\lim \limits_{x \to -3} \frac{6x^2 + 7x + 11}{5x - 7} = \square\\) (simplify your answer.)
\\(\bigcirc\\) b. the limit does not exist.

Explanation:

Step1: Substitute \( x = -3 \) into the numerator.

For the numerator \( 6x^2 + 7x + 11 \), substitute \( x = -3 \):
\( 6(-3)^2 + 7(-3) + 11 = 6\times9 - 21 + 11 = 54 - 21 + 11 = 44 \)

Step2: Substitute \( x = -3 \) into the denominator.

For the denominator \( 5x - 7 \), substitute \( x = -3 \):
\( 5(-3) - 7 = -15 - 7 = -22 \)

Step3: Divide the results of numerator and denominator.

Now, divide the numerator result by the denominator result: \( \frac{44}{-22} = -2 \)

Answer:

A. \( \lim\limits_{x\to -3} \frac{6x^2 + 7x + 11}{5x - 7} = -2 \)