Question 1

Which of the following statements about the parity of trigonometric functions is correct?

Accepted Answer

The sine function is odd and the cosine function is even.

Question 2

What is the derivative of $$f(x) = \sin x$$ with respect to $$x$$?

Accepted Answer

$$\frac{d}{dx} \sin x = \cos x$$

Question 3

Using the definition of the derivative and the limit $$\lim_{h 	o 0} \frac{\sin h}{h} = 1$$, what is $$\frac{d}{dx} \cos x$$?

Accepted Answer

$$-\sin x$$

Question 4

Which of the following is the correct double-angle formula for $$\sin(2x)$$?

Accepted Answer

$$\sin(2x) = 2 \sin x \cos x$$

Question 5

Evaluate $$\lim_{x 	o 0} \frac{\sin x}{x}$$ using L'Hospital's Rule.

Accepted Answer

1

Question 6

Which of the following is the derivative of $$f(x) = 	an x$$?

Accepted Answer

$$\sec^2$ x$$

Question 7

If $$f(x) = \cot x$$, what is $$\frac{d}{dx} f(x)$$?

Accepted Answer

$$-\csc^2$ x$$

Question 8

Which of the following is an indeterminate form that may require L'Hospital's Rule?

Accepted Answer

$$\frac{0}{0}$$

Question 9

Given $$\lim_{x 	o \infty} \frac{e^x}{x^3$}$$, what is the value of the limit?

Accepted Answer

$$\infty$$

Question 10

Which of the following is the correct identity for $$\sin(\frac{\pi}{2} - y)$$?

Accepted Answer

$$\sin(\frac{\pi}{2} - y) = \cos y$$

Question 11

If $$f(x) = \sec x$$, what is $$\frac{d}{dx} f(x)$$?

Accepted Answer

$$\sec x 	an x$$

Question 12

Which of the following is the correct Pythagorean identity?

Accepted Answer

$$\sin^2$ x + \cos^2$ x = 1$$

Question 13

Suppose $$f(x) = e$$^{\sin(3x^2)}$$. What is f$$'(x)$$?

Accepted Answer

$$e^{\sin(3x^2)}$$ \cdot 6x \$$cos(3x^2$$)$$

Question 14

Which of the following is the correct formula for $$\cos(2x)$$?

Accepted Answer

$$\cos(2x) = 2 \cos^2$ x - 1$$

Question 15

If $$\lim_{x 	o 1} \frac{\ln x}{x-1}$$, what is the value of the limit?

Accepted Answer

1

Question 16

Which of the following is the correct derivative of $$f(x) = \csc x$$?

Accepted Answer

$$-\csc x \cot x$$

Question 17

Which of the following is the correct sum formula for $$\sin(x+y)$$?

Accepted Answer

$$\sin(x+y) = \sin x \cos y + \cos x \sin y$$

Question 18

Which of the following is the correct expression for $$\sec(-x)$$?

Accepted Answer

$$\sec(-x) = \sec x$$

Question 19

If $$\lim_{x 	o \infty} \frac{x^2$}{e^x}$$, what is the value of the limit?

Accepted Answer

0

(L13) Derivatives of Trigonometric Functions and L'Hospital's Rule in Business Calculus

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