Math 16B HW 2 Review

Where to find amplitude of a sin function in the sin equation

asin(b(x-c))+d ?

Amplitude = a

Where to find period of a sin function in the sin equation

asin(b(x-c))+d ?

2pi / x

Where to find phase shift of a sin function in the sin equation

asin(b(x-c))+d ?

Set equation inside parenthesis equal to 0

b(x-c) = 0

What is phase shift of a sin function?

Horizontal span of the graph

Where to find vertical shift of a sin function in the sin equation

asin(b(x-c))+d ?

D (pos = up by d units, neg = down by d units)

Center of line is y = D

What information do you need to have to graph a sin function?

Amplitude, period, vertical shift, phase shift

What is chain rule?

F(g(x))’ = f’(g(x)) times g(x)’

What is the integral of 1/e^x?

-e^-x

What is the integral of e^-ax?

-1/a e^-ax

What is the derivative of ln3x?

3/3x dx

In the equation x³dx/ sqrt (3+ x²)dx, what is the u, and what is the dv? How do these terms come about?

By splitting up numerator x³ into x² and x/sqrt (3+x²)dx

u = x²

dv = x/sqrt (3+x²)dx

What is the integral of x/sqrt (3+x²)dx?

sqrt (3+x²)

When do you change the bounds of an integral when finding the volume? How do you do it?

When doing u sub, and do it by plugging into the u term

What is the integral of e^ax?

1/a e^ax

What is the chain rule?

f’(g(x)) = f’g(x) · g’(x)

What is the product rule?

F’(g(x)) = f’(x)g(x) + g’(x)f(x)