Q: Which of the following limits does NOT approach $$+\infty$$?

$$\lim\limits_{x \to 0^-} \dfrac{1}{x}$$

Question 1

Which of the following best describes an infinite limit?

Accepted Answer

A limit where the function increases or decreases without bound as $$x$$ approaches $$a.$$

Question 2

Evaluate $$\lim\limits_{x 	o 2} \dfrac{1}{(x-2)^2$}.$$

Accepted Answer

$$+\infty$$

Question 3

What does $$\lim\limits_{x 	o 0^+} \dfrac{1}{x}$$ represent?

Accepted Answer

The function approaches $$+\infty as$$ $$x$$ approaches $$0$$ from the right.

Question 4

Given $$\lim\limits_{x 	o a} f(x) = +\infty$$, which of the following is true?

Accepted Answer

The values of $$f(x)$$ can be made arbitrarily large by taking $$x$$ sufficiently close to $$a.$$

Question 5

Evaluate $$\lim\limits_{x 	o 0} \dfrac{1}{x^2$}.$$

Accepted Answer

$$+\infty$$

Question 6

Which of the following is a general property of $$\lim\limits_{x 	o a} \dfrac{1}{(x-a)^n}$$ for even $$n$$?

Accepted Answer

The limit is $$+\infty.$$

Question 7

Evaluate $$\lim\limits_{x 	o 4} \dfrac{1}{(x-4)^2$}.$$

Accepted Answer

$$+\infty$$

Question 8

Which of the following best describes the behavior of $$f(x) = \dfrac{1}{x} as$$ $$x$$ approaches $$0$$ from the left?

Accepted Answer

$$f(x)$$ approaches $$-\infty.$$

Question 9

Evaluate $$\lim\limits_{x 	o 0} \dfrac{\sin(x)}{x}.$$

Accepted Answer

$$1$$

Question 10

A medical researcher models the concentration of a drug in the bloodstream as $$C(t) = \dfrac{1}{(t-2)^2$}$$, where $$t is $$the time in hours after injection. What happens to the concentration as $$t$$ approaches $$2$$ hours?

Accepted Answer

The concentration increases without bound.

Question 11

Which of the following limits does NOT approach $$+\infty$$?

Accepted Answer

$$\lim\limits_{x 	o 0^-} \dfrac{1}{x}$$

Question 12

If $$\lim\limits_{x 	o a} f(x) = +\infty$$, what does this imply about the graph of $$f(x)$$ near $$x = a$$?

Accepted Answer

There is a vertical asymptote at $$x = a.$$

Study Notes: Infinite Limits in Calculus

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