General Stuff to Know

Question 1

sin(pi/4)

Answer 1

sqrt(2)/2

Question 2

cos(pi/4)

Answer 2

sqrt(2)/2

Question 3

tan(pi/4)

Answer 3

1

Question 4

sin(pi/2)

Answer 4

1

Question 5

cos(pi/2)

Answer 5

0

Question 6

sin(pi/6)

Answer 6

1/2

Question 7

cos(pi/6)

Answer 7

sqrt(3)/2

Question 8

sin(pi/3)

Answer 8

sqrt(3)/2

Question 9

cos(pi/3)

Answer 9

1/2

Question 10

sin(pi)

Answer 10

0

Question 11

cos(pi)

Answer 11

-1

Question 12

sin((3*pi)/2)

Answer 12

-1

Question 13

cos((3*pi)/2)

Answer 13

0

Question 14

Sign chart that goes -+

Answer 14

Min

Question 15

Sign chart that goes +-

Answer 15

Max

Question 16

Cost =

Answer 16

(price)(amount)

Question 17

How to do closed interval method

Answer 17

1. Find critical values
2. Plug in critical values and end points into f(x)
3. Whichever numbers are the highest and lowest are the x values for the min./max.

Question 18

How to do first derivative test

Answer 18

1. Find critical values
2. Set up a sign chart with f’(x)
3. Test random numbers next to the critical values
4. Use the positive and negative signs to determine if it is a max or min or neither

Question 19

How to do second derivative test

Answer 19

1. Find f’(x)
2. Set f’(x) = 0 and solve for critical values
3. Find f”(x)
4. Find f”(c)
5. If f”(c) < 0 then it’s a max
   If f”(c)>0 then it’s a min

Question 20

How to do optimization problem

Answer 20

1. State goals and constraints
2. Represent goal and constraint in equations
3. Use constraint equation to define goal equation with one variable.
4. Find f’(x) and find critical values
5. Use whatever method to

Question 21

How do you find where concavity changes?

Answer 21

1. Find f”(x)
2. Set f”(x)=0 and find inflection point
3. Use sign chart to determine if concavity is upward or downard (+ means up, - means down)

Question 22

Mean Value Theorem

Answer 22

If f(x) is continuous over [a,b], and f is differentiable over (a,b), then there will be some x=c where f’(c)=M_[a,b]

Question 23

L’Hospital’s rule

Answer 23

If lim_x-any f(x)/g(x) = 0/0 or DNE

lim_x-any f(x)/g(x) = lim_x-any f’(x)/g’(x)

lim_x-any h(x) = lim_x-any f(x)/g(x)

Question 24

Things to remember about L’hospital’s rule

Answer 24

1. Only works if answer is indeterminate
2. Always check if answer is indeterminate
3. Doesn’t always work first time, so keep trying until you get it
4. Sometimes you will get into an infinite loop after applying L’hospital over and over

Question 25

Finding values of x within certain error

Answer 25

1. |f(x) - L(x)| =< decimal for error goal 2. Remove absolute value and get compound inequality 3. Use calculator to find x values for when f(x)-L(x) intersects with error goals 4. Write intersection values as interval

Question 26

How to do linear approximation

Answer 26

1. Define as function of x 2. Find derivative of x 3. Take known value close to value in original problem and use it to find the equation for the line at that section 4. Take value from original problem and plug into equation for line

Question 27

When is cos(x) = 1?

Answer 27

2(pi)n

Question 28

When is sin(x)=1?

Answer 28

pi/2 +- 2n(pi)

Question 29

When is cos(x) = 0?

Answer 29

(pi/2) +- pi(n)

Question 30

When is sin(x) = 0?

Answer 30

(pi)n

Question 31

What coordinate value on the unit circle does sin represent?

Answer 31

y-coordinate

Question 32

What coordinate value on the unit circle does cos represent?

Answer 32

x-coordinate

Question 33

Area of equilateral triangle

Answer 33

A = (sqrt(3) * x^2) /4

Question 34

Finding critical values

Answer 34

1. Find domain of f(x) (just graph it) 2. Find f'(x) 3. Find where f'(x) = 0 or where f'(x) = DNE 4. x values that are within domain are critical values

Question 35

Functions where you have to worry about domain

Answer 35

1. Square root/even radical functions 2. Log functions 3. Rational functions