Find the limits. if the limit does not exist, state it. In each part show your c

Question

Find the limits. if the limit does not exist, state it. In each part show your calculations and circle the answer.

\frac{x^{2} - 4 x + 4}{x^{2} + x - 6}

Answer 1

Given:

f (x) = \frac{x^{2} - 4 x + 4}{x^{2} + x - 6}

Left hand limit

lim_{x \to - 3^{-}} f (x) = lim_{x \to - 3^{-}} \frac{x^{2} - 4 x + 4}{x^{2} + x - 6}

lim_{x \to - 3^{-}} f (x) = \infty

The function grows without bound.
Right hand limit

lim_{x \to - 3^{+}} f (x) = lim_{x \to - 3^{+}} \frac{x^{2} - 4 x + 4}{x^{2} + x - 6}

lim_{x \to - 3^{+}} f (x) = - \infty

The function decreases without bound.

lim_{x \to - 3^{-}} f (x) \neq lim_{x \to - 3^{+}} f (x)

Since the corresponding two-sided limits are not equal,

lim_{x \to - 3} \frac{x^{2} - 4 x + 4}{x^{2} + x - 6}

does not exist.

Answer 2

Jeffrey Jordon

Answered 2022-06-26 Author has 2262 answers

Answer is given below (on video)

Expert Answer