Q: Which of the following statements about infinite limits is TRUE?

If $$\lim_{x \to a} f(x) = \infty$$, then $$f(x)$$ increases without bound as $$x$$ approaches $$a.$$

Q: Which of the following limits represents an infinite limit?

$$\lim_{x \to 0} \frac{1}{x^2$}$$

Question 1

Evaluate the following limit: $$\lim_{x 	o 2} \frac{x^2$ - 4}{x - 2}$$

Accepted Answer

$$4$$

Question 2

Which of the following best describes the Squeeze Theorem?

Accepted Answer

If $$f(x) is $$squeezed between $$g(x)$$ and $$h(x)$$, and $$\lim_{x 	o a} g(x) = \lim_{x 	o a} h(x) = L$$, then $$\lim_{x 	o a} f(x) = L.$$

Question 3

Compute $$\lim_{x 	o 0} \frac{\sin x}{x}.$$

Accepted Answer

$$1$$

Question 4

Which of the following limits does NOT exist?

Accepted Answer

$$\lim_{x 	o 0} \frac{1}{x}$$

Question 5

Evaluate $$\lim_{x 	o 0^+} \ln x.$$

Accepted Answer

$$-\infty$$

Question 6

Suppose $$-x^2$$ \leq f(x) \leq $$x^2$$ for all $$x$$ near $$0. $$What is $$\lim_{x 	o 0} f(x)$$?

Accepted Answer

$$0$$

Question 7

Which of the following statements about infinite limits is TRUE?

Accepted Answer

If $$\lim_{x 	o a} f(x) = \infty$$, then $$f(x)$$ increases without bound as $$x$$ approaches $$a.$$

Question 8

Evaluate $$\lim_{x 	o 0} \frac{e^x - 1}{x}.$$

Accepted Answer

$$1$$

Question 9

A hospital monitors the concentration $$C(t) of a $$drug in a patient’s bloodstream, modeled by $$C(t) = \frac{10}{t}$$ for $$t \u003e 0. $$What happens to $$C(t) as$$ $$t 	o 0^+$$?

Accepted Answer

$$C(t)$$ approaches $$\infty$$

Question 10

Evaluate $$\lim_{x 	o 3} \frac{x^2$ - 9}{x - 3}.$$

Accepted Answer

$$6$$

Question 11

Which of the following is a correct application of the Squeeze Theorem?

Accepted Answer

If $$-x \leq \sin x \leq x$$ for all $$x$$ near $$0$$, then $$\lim_{x 	o 0} \sin x = 0.$$

Question 12

Evaluate $$\lim_{x 	o 0} x \sin\left(\frac{1}{x}ight).$$

Accepted Answer

$$0$$

Question 13

Which of the following limits represents an infinite limit?

Accepted Answer

$$\lim_{x 	o 0} \frac{1}{x^2$}$$

Question 14

Evaluate $$\lim_{x 	o 0^+} \frac{1}{x}.$$

Accepted Answer

$$\infty$$

Question 15

A chemical reaction rate is modeled by $$R(t) = \frac{5}{t^2$}$$ for $$t \u003e 0. $$What is $$\lim_{t 	o 0^+} R(t)$$?

Accepted Answer

$$\infty$$

Study Notes: Limits, Squeeze Theorem, and Infinite Limits

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