Final exam

Question 1

2.1

average velocity

Answer 1

change in distance/ change in time

Question 2

2.1

instantaneous velocity

Answer 2

1st derivative of a position equation

Question 3

acceleration

Answer 3

2nd derivative of position function

Question 4

2.1

slope using two points

Answer 4

Y2-Y1/X2-X1

Question 5

Point slope form

Answer 5

(Y-Y1)=m(X-X1)

Question 6

2.2

If a limit as X approaches 3+ = 4 and the limit as X approaches 3- = -4 does the limit exist?

Answer 6

no the limit does not exist, must agree on both sides

Question 7

definition of a vertical asymptote

Answer 7

limit as x approaches a of f(x) = positive or negative infinity

Question 8

a non zero number/ 0 =

Answer 8

+- infinity

Question 9

2.5

what are the three points needed for a function to be continunous?

Answer 9

1. f(a) is defined
2. limit as x approaches a = f(a)
3. the limit as x approaches a exsits (cant be one sided)

Question 10

domain of polynomials

Answer 10

All reals

Question 11

domain of a rational function

Answer 11

where the denominator does not = 0

Question 12

domain of trig functions

Answer 12

all reals

Question 13

domain of exponential functions

ex: e^x, 2^x, 7^x

Answer 13

all reals

Question 14

domain of logarithmic functions

ex: ln, log

Answer 14

(0, infinity)

Question 15

2.5

Intermediate value theorum

Answer 15

on a closed interal from [a,b] a continuous function will have a value for f(c) somewhere bc/ it is continuous

Question 16

domain of odd and even root functions

Answer 16

odd (all reals)
even [o, infinity)

Question 17

2.7

definition of a derivative

Answer 17

• lim as h approaches 0 f(a+h) -f(a)/h = f(x)-f(a)/x-a
• the slope of the tangent line

Question 18

2.8

What does it mean to be differentiable?

Answer 18

if a function is differentibale at a point that means the derivative exists there and it is continuous

not differentiable where the derivative cannot exist

Question 19

2.8

True or false? if x= a is cont then f is differentiable at x=a

Answer 19

false, you cant swap the sentence and still have it be true

Question 20

3.1

derivative of b^x=

Answer 20

b^x *ln(b)

Question 21

3.5

Implicit differentation

Answer 21

taking the derivative on both sides with the assumption that y is a function/ y= f(x)

Question 22

3.10

differentials

Answer 22

dy=f’(x)* dx

use this for measurement error problems

Question 23

3.10

surface area of a cube

Answer 23

6a^2

Question 24

4.1

extreme value therorum

Answer 24

if f(x) is continous on a closed interval then f(x0 has an absolute max and min on that interval

on closed intervals you can choose the ends

Question 25

4.1

the point is a critical point if…

Answer 25

f’(c) = 0 or f’(c) DNE

Question 26

4.1

if f(x) has a local max or local min at x=c then f’(c) = 0 or f’(c) DNE

Answer 26

fermats theorum

CRITICAL POINT DOES NOT =. LOCAL MIN/MAX

Question 27

4.2

Rolles theorum

Answer 27

1. f(a) =f(b)
2. f(x) is cont on (a,b)
3. f(x) is differentiable on (a,b)
   - f’(c) = 0

use to prove at most one solution

Question 28

4.2

Mean Value Theorum

Answer 28

1. f is cont on (a,b)
2. f is differentiable on (a,b)
   - f’(c) = f(b)-f(a)/b-a

average rate of change from a to b

Question 29

4.3

Inflection points

Answer 29

where concavity changes from up or down or vice versa

Question 30

4.4

what should you do if you get the indeterminate form 0/0 or infinity/infinity

Answer 30

take the derivative of the top and bottom separatley

L’hopital

Question 31

4.4

What should you do if you get the indeterminate form 0 * infinity

Answer 31

f(x)/ (1/g(x))

Question 32

4.4

what should you do if you get the indeterminate form infinity - infinity

Answer 32

find a common denominator or factor

Question 33

4.4

what should you do if you get the indeterminate form of 0^0, infinity^0 or 1^infinity

Answer 33

e^ln(fx) and bring the limit up

Question 34

4.5

how do you find the x and y intercepts of a function?

Answer 34

x int: 0= f(x)
y-int: y= f(0)

Question 35

4.5

how do you determine symmetry for a function?

Answer 35

odd symmetry: f(-x)= -(f(x))
even: f(-x)=f(x)

Question 36

4.9

Never forget to add what after the most general antiderivative?

Answer 36

+ C

Question 37

Derivative of a log

log(x) base a

Answer 37

1/x*ln(a)

Question 38

5.1

What does it mean to use right end points?

Answer 38

to use the right most values, leaving out the lowest value
- ex: of your points are 0, 1/2, 1 and 3/2 for right most you wouldnt use 0

Question 39

5.2

What does it mean to use leftmost end points?

Answer 39

use the left most values and the lowest value
- ex: if your values are 0,2,4,6 then you wouldnt use 6

Question 40

5.1

How do you find your change in x?

[a,b] w/ n number of rectangles

Answer 40

b-a/n

Question 41

5.3

What does the Fundamental theorum of calculus let you do?

Answer 41

if f is cont on [a,b] then the intetral from a-b on f(x) is any antiderivatve F(b)- F(a)

Question 42

definition of a absolute maximum

Answer 42

x=b is a local max of f(x) if f(b)> f(x) for any x near b

Question 43

definition of an absolute minimum

Answer 43

x=a is an absolute minimum if f(a)<f(x) for all x in the domain of f

Question 44

5.3

FTC pt 2

Answer 44

if f(x) is cont then the integral from a to b is = any antiderivative F(b)-F(a)

Question 45

5.5

What should you never do when using the u sub rule for integrals?

Answer 45

u=x

it wont do anything