Question 1

Which of the following intervals represents the solution set to the inequality $$|2x - 5| \u003c 7$$?

Accepted Answer

Question 2

Let $$f(x) = \begin{cases} x^2$ & x \u003c 1 \ 2x + 1 & x \geq 1 \end{cases}. $$Which of the following statements is true about the continuity of $$f(x) at$$ $$x = 1$$?

Accepted Answer

$$f(x) is $$not continuous at $$x = 1$$ because $$\lim\limits_{x 	o 1^-} f(x) 
eq \lim\limits_{x 	o 1^+} f(x)$$

Question 3

Which of the following is the correct expansion of $$(2x - 3)^4$ using the Binomial Theorem?

Accepted Answer

$$16x^4$$ - $$96x^3$$ + $$216x^2 - 216x + 81$

Question 4

A patient’s temperature $$T (in$$ $$^\circC) is $$modeled by $$T(t) = 37 + 2e$$^{-0.5t}$$, where t$ is hours after medication. What is the rate of change of temperature after 2 hours?

Accepted Answer

$$-e^{-1}$$ $$^\circC/$$hour

Question 5

Which of the following is the correct derivative of $$y = \ln(\sin x)$$ for $$0 \u003c x \u003c \pi$$?

Accepted Answer

$$\cot x$$

Question 6

Suppose $$f(x) = x^3$ - 3x + 2. $$Which of the following statements about the critical points of $$f(x) is $$correct?

Accepted Answer

There are two critical points at $$x = 1$$ and $$x = -1$$

Question 7

Which of the following is the correct solution to the equation $$2^{x+1} = 8$?

Accepted Answer

$$x = 2$$

Question 8

A ball is thrown upward with velocity $$v(t) = 20 - 9.8t. At $$what time does the ball reach its maximum height?

Accepted Answer

$$t = 2.04$$ seconds

Question 9

Which of the following is the correct domain of the function $$f(x) = \sqrt{3 - x}$$?

Accepted Answer

$$(-\infty, 3]$$

Question 10

If $$\lim\limits_{x 	o 2} f(x) = 5$$ and $$\lim\limits_{x 	o 2} g(x) = -3$$, what is $$\lim\limits_{x 	o 2} [2f(x) - 3g(x)]$$?

Accepted Answer

$$19$$

Question 11

Which of the following is the correct result of rationalizing the denominator of $$\frac{5}{\sqrt{2} + 1}$$?

Accepted Answer

$$\frac{5(\sqrt{2} - 1)}{1}$$

Question 12

Which of the following is the correct derivative of $$y = e$$^{2x}$$ \sin x$$?

Accepted Answer

$$e^{2x}(2$$\sin x + \cos x)$$

Question 13

Which of the following is the correct solution to the inequality $$\log_2$(x - 1) \u003e 3$$?

Accepted Answer

$$x \u003e 8$$

Question 14

Which of the following is the correct value of $$\sin(\frac{\pi}{6})$$?

Accepted Answer

$$\frac{1}{2}$$

Question 15

Let $$f(x) = x^2$ and g(x) = x + 1$. What is (f$$ \circ g)(2)$$?

Accepted Answer

$$9$$

Question 16

Which of the following is the correct result of applying the chain rule to $$y = \cos(3x^2$)$$?

Accepted Answer

$$-6x \sin(3x^2$)$$

Question 17

Which of the following is the correct result of $$\sum\limits_{k=1}^{4} (2k + 1)$$?

Accepted Answer

$$20$$

Question 18

Which of the following is the correct contrapositive of the statement: 'If a number is even, then it is divisible by 2'?

Accepted Answer

If a number is not divisible by 2, then it is not even.

Question 19

Which of the following is the correct value of $$\lim\limits_{x 	o 0} \frac{\sin x}{x}$$?

Accepted Answer

$$1$$

Question 20

Which of the following is the correct anti-derivative of $$f(x) = 3x^2$?

Accepted Answer

$$x^3 + C$

MATH130W1 Calculus Syllabus and Core Topics Study Guide

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