Explained: "Find the limits. if the limit does not..."

preprekomW

Answered question

2021-11-06

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}

Aniqa O'Neill

Skilled2021-11-07Added 100 answers

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.

Jeffrey Jordon

Expert2022-06-26Added 2605 answers

Answer is given below (on video)

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