Q: A graph of $$f(x)$$ has a jump discontinuity at $$x = 2. $$Which of the following statements is true?

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

Q: A function $$h(x) is $$continuous everywhere except at $$x = 0. $$Which of the following is true?

$$\lim_{x \to 0} h(x)$$ may not exist

Q: A function $$f(x) is $$defined by a graph with a removable discontinuity at $$x = -2. $$What does this mean?

$$\lim_{x \to -2} f(x)$$ exists but $$f(-2) is $$not equal to the limit

Question 1

A hospital monitors the concentration of a drug in a patient's bloodstream, modeled by the function $$C(t) = 5e$$^{-0.2t}$$, where t$ is in hours. What is $$\lim_{t 	o \infty} C(t)$$?

Accepted Answer

$$0$$

Question 2

Evaluate $$\lim_{x 	o 2} \dfrac{x^2$ - x - 6}{x^2$ - x - 2}.$$

Accepted Answer

$$2$$

Question 3

A biologist models the population of a species by $$P(x) = \sqrt{x^2$ + 3x + 6}. $$What is $$\lim_{x 	o -3} P(x)$$?

Accepted Answer

$$3$$

Question 4

Find $$\lim_{x 	o 2} \dfrac{\sqrt{x+8} - \sqrt{8}}{x - 2}.$$

Accepted Answer

$$\dfrac{1}{4}$$

Question 5

A chemical reaction rate is given by $$R(x) = \dfrac{2}{5 + x}. $$What is $$\lim_{x 	o 0} R(x)$$?

Accepted Answer

$$\dfrac{2}{5}$$

Question 6

Evaluate $$\lim_{x 	o \infty} \dfrac{x^2$ + 10x + 2}{2x^2$ + x^2$}.$$

Accepted Answer

$$\dfrac{1}{3}$$

Question 7

A patient’s temperature is modeled by $$T(x) = 8 - x. $$What is $$\lim_{x 	o 8} T(x)$$?

Accepted Answer

$$0$$

Question 8

Evaluate $$\lim_{x 	o 1} \dfrac{x + 3}{x^2$ - x - 2}.$$

Accepted Answer

$$-4$$

Question 9

A function $$f(x) is $$defined as $$f(x) = \dfrac{1}{x}$$ for $$x 
eq 0. $$What is $$\lim_{x 	o 0^+} f(x)$$?

Accepted Answer

$$\infty$$

Question 10

Given $$\lim_{x 	o a} f(x) = 3$$ and $$\lim_{x 	o a} g(x) = 2$$, evaluate $$\lim_{x 	o a} (f(x) + 2g(x)).$$

Accepted Answer

$$7$$

Question 11

Evaluate $$\lim_{x 	o 0} \left( \dfrac{1}{x} - \dfrac{1}{x+1} ight).$$

Accepted Answer

$$\infty$$

Question 12

A graph of $$f(x)$$ has a jump discontinuity at $$x = 2. $$Which of the following statements is true?

Accepted Answer

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

Question 13

A function $$h(x) is $$continuous everywhere except at $$x = 0. $$Which of the following is true?

Accepted Answer

$$\lim_{x 	o 0} h(x)$$ may not exist

Question 14

Evaluate $$\lim_{x 	o 3} \dfrac{x^2$ - x - 6}{x^2$ - x - 2}.$$

Accepted Answer

$$\dfrac{2}{4}$$

Question 15

A function $$f(x) is $$defined by a graph with a removable discontinuity at $$x = -2. $$What does this mean?

Accepted Answer

$$\lim_{x 	o -2} f(x)$$ exists but $$f(-2) is $$not equal to the limit

Question 16

Evaluate $$\lim_{x 	o 0} \dfrac{8 - x}{8 - x}.$$

Accepted Answer

$$1$$

Question 17

A function $$f(x) is $$defined as $$f(x) = \sqrt{x^2$ + 3x + 6}. $$What is the domain of $$f(x)$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 18

A function $$f(x) is $$defined as $$f(x) = \dfrac{1}{x^2$}. $$What is $$\lim_{x 	o 0} f(x)$$?

Accepted Answer

$$\infty$$

Question 19

Evaluate $$\lim_{x 	o 0} \dfrac{\sin x}{x}.$$

Accepted Answer

$$1$$

Question 20

A function $$f(x) is $$defined as $$f(x) = x^2$ + 3x + 6. $$What is $$\lim_{x 	o -3} f(x)$$?

Accepted Answer

$$6$$

Limits and Continuity: Calculus Practice Exam Study Guide

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