Trig Derivatives

Question 1

What is the limit of $\frac{\sin x}{x}$ as $x$ approaches $0$?

Accepted Answer

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

Question 2

What is the limit of $\frac{1 - \cos x}{x}$ as $x$ approaches $0$?

Accepted Answer

$\lim_{x 	o 0} \frac{1 - \cos x}{x} = 0$

Question 3

What is the limit of $\frac{1 - \cos x}{x^2}$ as $x$ approaches $0$?

Accepted Answer

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

Question 4

What is the limit of $\frac{	an x}{x}$ as $x$ approaches $0$?

Accepted Answer

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

Question 5

What is the derivative of $\sin x$?

Accepted Answer

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

Question 6

What is the derivative of $\cos x$?

Accepted Answer

$\frac{d}{dx}[\cos x] = -\sin x$

Question 7

What is the derivative of $	an x$?

Accepted Answer

$\frac{d}{dx}[	an x] = \sec^2 x$

Question 8

What is the derivative of $\csc x$?

Accepted Answer

$\frac{d}{dx}[\csc x] = -\csc x \cot x$

Question 9

What is the derivative of $\sec x$?

Accepted Answer

$\frac{d}{dx}[\sec x] = \sec x 	an x$

Question 10

What is the derivative of $\cot x$?

Accepted Answer

$\frac{d}{dx}[\cot x] = -\csc^2 x$

Alle Karten