Final Exam Review

Probability

100

What is the sample space of tossing a coin?

S={H,T}

200

Write the Probability of A and not B

(AnB^C)

300

Sure! Here's a conditional probability problem for you

In a deck of 52 playing cards, there are 13 cards of each suit (hearts, diamonds, clubs, spades). Suppose you randomly draw two cards from the deck without replacement.

 What is the probability that the second card is a heart, given that the first card drawn is a heart?

4/17

400

A factory produces light bulbs, and 95% of them pass quality control while 5% are defective. A quality control inspector randomly selects a bulb from a batch, and if the bulb is defective, the inspector replaces it. If the bulb is not defective, the inspector keeps it.

What is the probability that the inspector replaced the bulb, given that the bulb is defective?

1

500

What does mutually exclusive mean?

No intersection

Differential Equations

100

What is the difference between Linear and Seperable?

Separable you can group y and x terms on both sides, Linear needs to be in standard form. 

200

Solve dy/dx = 2x/y. 

y=± Square root 2x²+C

300

Sove dx/dy+3y=6x

y=2x−2/3+Ce^-3x

400

Solve x dy/dx +2y =4/x

y=4/x +16/x²

500

What is e^{S4/x dx}

x⁴

Functions of Several Variables

100

Find f(4, -2) when f(x,y)= (x-3y)/(x²+y²)

1/2

200

Find f(3,-1,2) when f(x,y,z)= x²-2y³+6z²

35

300

Find f_x (x,y)

f(x,y)= 6x³y^-2-4x^-1y²

18x²y^-2+4x^-2y²

400

What is a level curve of a function f(x,y)?

A level curve is the set of all points (x,y) in the plane where the function f(x,y) takes the same constant value. f(x,y)=c

500

For the function f(x,y)=x²+y² ,what shape will the level curves look like?

The level curves for the function are concentric circles centered at the origin.

Integration/Differentiation

100

Derivative of y=5x³+4x²-8x+3

15x²+8x-8

200

Derivative of [x²sinx]

2x(sinx)+x²(cosx)

300

Find the Integral from 2 to 1 of 6x² dx

4

400

Find the Integral of 4xe^x2dx

2e^x2+c

500

d/dx (5x+6)/(3x-7)

(3x-7)(5)-(5x+6)(3)/(3x-7)²