Test 3

Question 1

What is the equation for approximations?

Answer 1

f(x)=f(a)+f’(a)(x-a)

Question 2

L’Hospital’s rule:
if lim x–>a f(x)/g(x)= “0”/0 then lim x–> a is

Answer 2

f’(x)/ g’(x)= L

Question 3

L’Hospital’s rule:
lim x–>a f(x)/ g(x) = “infinity”/ infinity= lim x–>a=

Answer 3

f’(x)/ g’(x)=L

Question 4

If it is L’hospital’s rules = 0 times infinity you put something in the _______ to make it divided by

Answer 4

denominator

Question 5

If it is infinity minus infinity, what rules do you have to do?

Answer 5

1. algebra
2. L’hospital’s rule

Question 6

If it is 0^0, 1^infinity, infinity^0 what are the rules?

Answer 6

1. LN
2. algebra
   3.l’hospital’s

Question 7

To find concavity you have find where f’‘(x)=

Answer 7

0

Question 8

If there is no denominator there typically no vertical asymptotes unless the function is ______ or _______

Answer 8

logarithmic function or piecewise defined function

Question 9

when it is integral
sin will be

Answer 9

-cos

Question 10

What is the equation for M.V.T?

Answer 10

f’(c)= f(b)- f(a)/ b-a

Question 11

With M.V.T, it is for continuous and differentiable functions (f(x)) on a ______ interval

Answer 11

closed

Question 12

With M.V.T, the _______ rate of change is at some point equal to the _______ rate of change of the function over the interval

Answer 12

instantaneous, average

Question 13

What is the concavity is
f’‘(x)> 0

Answer 13

concave up

Question 14

What is the concavity if f’‘(x) < 0

Answer 14

concave down

Question 15

_______ point is where concavity switches

Answer 15

inflection

Question 16

What is the equation for L’Hopital’s Rule?

Answer 16

lim x–>a f(x)/ g(x)= lim x–>a f’(x)/ g’(x)

Question 17

With L’Hopital’s rule if it is 0 times infinity how do you rewrite the function?

Answer 17

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

Question 18

L’ H’ rules if it is infinity- infinity how do you rewrite it?

Answer 18

combine terms under common denominator

Question 19

L’ H’s rule, ^0, 1^ infinity how do you rewrite it?

Answer 19

rewrite using logarithms

Question 20

With graphing, what does domain, range, x-intercepts and y-intercepts come from?

Answer 20

f(x)

Question 21

With graphing, where does increasing, decreasing, and critical points come from?

Answer 21

f’(x)

Question 22

With graphing, where does concavity and inflection points come from?

Answer 22

f’‘(x)

Question 23

What are the steps for applied maxs/ mins?

Answer 23

1. read problem
2. draw picture
3. write and equation
4. make one variable
   5.differentiate
5. find C.P
6. find max/mins
7. answer question

Question 24

For oscilating revenue functions what is the equation for r(x)?

Answer 24

r(x)= p(x)(x)

Question 25

With revenue oscilating P(x) the profit is always what (equation)?

Answer 25

P(x)= R(x)- C(x) (revenue- cost)

Question 26

What is the equation for Newton’s Method?

Answer 26

Xn+1= Xn- f(Xn)/ f’(Xn)

Question 27

With Newton’s rule when do you stop?

Answer 27

When the approximations are within a 0.0001 difference

Question 28

What is the fundamental theorem of calc?

Answer 28

integral a b f(x)dx= F(b)-F(a)

Question 29

Trig Rules with Integrals:
sinxdx=

Answer 29

-cosx+C

Question 30

Trig Rules with Integrals:
sin(Kx)dx=

Answer 30

-1/k cos[kx] +c

Question 31

Trig Rules with Integrals:
cosxdx

Answer 31

sinx+C

Question 32

Trig Rules with Integrals:
cos(kx)dx=

Answer 32

1/k sinkx +C

Question 33

Trig Rules with Integrals:
sec^2xdx=

Answer 33

tanx +C

Question 34

Trig Rules with Integrals:
sec^2(Kx)dx

Answer 34

1/k tan(kx) +C

Question 35

Trig Rules with Integrals:
csc^2x dx=

Answer 35

• cot(x)+C

Question 36

Trig Rules with Integrals:
e^kxdx

Answer 36

1/ke^kx+C`

Question 37

What is the FTC II?

Answer 37

F’(x)= f(x)

Question 38

What is the equation for net change?

Answer 38

the integral of a to be f’(x)dx

Question 39

What is the equation for integration by parts?

Answer 39

udw= uw- wdu

Question 40

If the integral is b^xdx what is it then?

Answer 40

b^x/ lnb +C

Question 41

1/ square root (1-x^2) =

Answer 41

arcsinx

Question 42

1/ (1+x^2)

Answer 42

arctanx

Question 43

1/ [x] square root (x^2 -1)

Answer 43

arcsecx

Question 44

b sigma i=a =c what is it/

Answer 44

c(b-a +1)

Question 45

n sigma i=1 i=

Answer 45

n(n+1)/2

Question 46

n sigma i=1 i^2 =

Answer 46

n(n+1)( 2n+1) /6