$$\lim_{x \to 2} f(x)$$ does not exist

Question 1

Given $$f(x) = \frac{x^2$ - 4}{x - 2}$$ for $$x 
eq 2$$, what is $$\lim_{x 	o 2} f(x)$$?

Accepted Answer

$$4$$

Question 2

Which of the following statements best describes the meaning of $$\lim_{x 	o c} f(x) = L$$?

Accepted Answer

As $$x$$ gets very close to $$c$$, $$f(x)$$ gets very close to $$L.$$

Question 3

If $$\lim_{x 	o 2^-} f(x) = 1$$ and $$\lim_{x 	o 2^+} f(x) = 3$$, what can you conclude about $$\lim_{x 	o 2} f(x)$$?

Accepted Answer

$$\lim_{x 	o 2} f(x)$$ does not exist

Question 4

Evaluate $$\lim_{x 	o 3} \frac{x^2$ - 5x + 6}{x - 3}.$$

Accepted Answer

$$1$$

Question 5

Which of the following is a necessary condition for the overall limit $$\lim_{x 	o c} f(x) to $$exist?

Accepted Answer

The left and right limits at $$c$$ are equal and finite.

Question 6

Given $$\lim_{x 	o c} f(x) = L$$ and $$\lim_{x 	o c} g(x) = M$$, what is $$\lim_{x 	o c} [f(x) + g(x)]$$?

Accepted Answer

$$L + M$$

Question 7

Evaluate $$\lim_{x 	o 36} \frac{\sqrt{x} - 6}{x - 36}$$ using the rationalizing technique.

Accepted Answer

$$12$$

Question 8

If $$\lim_{x 	o 4} \frac{x + 2}{\sqrt{x} - 2}$$, what is the limit?

Accepted Answer

$$\infty$$

Question 9

Suppose $$f(x) is $$defined as $$f(x) = \frac{x^2$ - 6x - 7}{x^2$ + 3x + 2}. $$What is $$\lim_{x 	o -1} f(x)$$?

Accepted Answer

$$-8$$

Question 10

For the piecewise function $$f(x) = \begin{cases} 10 - 2x & x \u003c 3 \ x^2$ - x & x \geq 3 \end{cases}$$, what is $$\lim_{x 	o 3} f(x)$$?

Accepted Answer

Does not exist

Question 11

If $$\lim_{x 	o 2} f(x) = 4$$ but $$f(2) is $$undefined, which of the following is true?

Accepted Answer

The limit exists even if the function is undefined at $$x = 2.$$

Question 12

Evaluate $$\lim_{x 	o 2} \frac{x + 5}{x^2$ - x - 2}.$$

Accepted Answer

$$\infty$$

Question 13

Which of the following best describes an indeterminate form?

Accepted Answer

Both numerator and denominator approach zero.

Question 14

If $$\lim_{x 	o 0^-} f(x) = 2$$ and $$\lim_{x 	o 0^+} f(x) = 2$$, but $$f(0) is $$undefined, what is $$\lim_{x 	o 0} f(x)$$?

Accepted Answer

$$2$$

Question 15

Which of the following is true about vertical asymptotes in the context of limits?

Accepted Answer

The limit does not exist at the vertical asymptote.

Limits and Their Properties: Business Calculus Study Guide

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