Math 142 Final Review

First third

100

What would you pick as U for integral (x/root(4+x^2))

4+x^2

200

How do you find the absolute Max?

Take the first derivative, find roots, use sign chart.

Bonus: How do you find roots for fractions, LN(x), e^x

300

Set up:

Find Area of region bound by y = sin(x), y = cos(x), x = 0 and x = pi/2

Integral of cos(x) - sin(x) from 0 to pi/4 + integral of sin(x) - cos(x) from pi/4 to pi/2

400

What are all L'Hôpitals Indeterminates

0/0

inf/inf

0*inf

inf - inf

0^0

1^inf

inf^0

500

Use the washer Method to SETUP this problem. 

Find Volume of y = x, y=x^2 rotated around x=-1

Integral of (pi(1+root(y))^2 - pi (1+y)^2) from 0 to 1

Second third

100

What is the integration by parts equation?

 UV - integral of VDU

200

When do you use logarithmic differentiation?

When you are trying to take the derivative of a complex fraction, or when you have something to the power of x

300

Find domain of sin^-1 (X^2 - 1)

D: [-root(2), root(2)]

400

Four types of partial fraction decomposition and write them out.

Type 1: Linear, non-repeated

Type 2: Linear Repeating

Type 3: Irreducible quadratic, non-repeating

Type 4: Irreducible quadratic, repeating

500

Match Radical with strategy and tell me Identity

1.) Root (a^2 + x^2)

2.) Root (a^2 - x^2)

3.) Root (x^2 - a^2 )

1.) x = Tan(theta)

2.) x = sin(theta)

3.) x = sec(theta)

Last third

100

Which is the most accurate: Simpson's Rule, Midpoint Rule or Trapezoidal Rule?

Simpson's Rule

200

Increasing the number of subintervals generally causes the error in numerical integration to do what?

Decrease

300

The Trapezoidal Rule error bound depends on the maximum value of which derivative, what about Simpson's Rule?

Trapezoidal Rule: Second Derivative

Simpson's Rule: Fourth Derivative

400

In comparison theory, what should you compare 5x+2/x^3+9 to?

1/x^3

500

A numerical approximation using Simpson's Rule has error bound Es <= K/N^4, By what factor must nnn increase to reduce the error by a factor of 81?

n = 3

Pick a Strategy and set up

100

Slide 1

Integration by Parts

200

Slide 2

Partial Fraction Decomposition

300

Slide 3

Integration by Parts

400

Slide 3

Improper Integral

500

Slide 4

U-sub and Trig Sub

Misc

100

Graph y = x^3

Look at Desmos

200

What is the strategy to pick u for integration by parts

ILATE

Inverse Trig

Log

Algebraic

Trig

Exponents

300

What is the derivative and integral of B^x

Derivative B^x ln(b)

Integral B^x/ln(b) + C

400

What is the domain of Ln(X^2 +X)

(-inf,-1] U [0,inf)

500

Find the arc length of y = (2/3)x^3/2 on the interval 0<x<3

14/3