Exam 1

Question 1

integral of 1/x

Answer 1

ln abs value x

Question 2

integral e to the x

Answer 2

e to the x

Question 3

integral sinx

Answer 3

-cosx

Question 4

integral sec^2x

Answer 4

tanx

Question 5

integral secxtanx

Answer 5

secx

Question 6

integral secx

Answer 6

ln I secx + tanx I

Question 7

integral tanx

Answer 7

ln I secx I

Question 8

integral 1/(sq. root 1-x^2)

Answer 8

arcsinx (sin-1x)

Question 9

integral b^x

Answer 9

b^x/lnb

Question 10

integral cosx

Answer 10

sinx

Question 11

integral csc^2x

Answer 11

-cotx

Question 12

integral cscxcotx

Answer 12

-cscx

Question 13

integral cscx

Answer 13

ln I cscx-cotx I

Question 14

integral cotx

Answer 14

ln I sinx I

Question 15

integral 1/x^2 +1

Answer 15

arctanx (tan-1x)

Question 16

sin^2x + cos^2x

Answer 16

1

Question 17

tan^2x +1 =

Answer 17

sec^2x

Question 18

1 + cot^2x =

Answer 18

csc^2x

Question 19

sin2x

Answer 19

2sinxcosx

Question 20

cos2x

Answer 20

cos^2x - sin^2x

2cos^2x-1

Question 21

sin^2x =

Answer 21

1/2 (1-cos2x)

Question 22

cos^2x=

Answer 22

1/2(1+cos2x)

Question 23

tan^2x=

Answer 23

(1-cos2x)/(1+cos2x)

Question 24

volume of a sphere

Answer 24

v= 4/3 pi r^3

Question 25

area of a pyramid or cone

Answer 25

v= 1/3 (area of base) height

Question 26

volume of prism or cylinder

Answer 26

v= (area of base) height

Question 27

cos (0)

Answer 27

1

Question 28

cos(pi/6)

Answer 28

(sq root 3)/2

Question 29

cos(pi/4)

Answer 29

(sq root 2)/2

Question 30

cos(pi/3)

Answer 30

1/2

Question 31

cos(pi/2)

Answer 31

0

Question 32

cos pi

Answer 32

-1

Question 33

sin(0)

Answer 33

0

Question 34

sin(pi/6)

Answer 34

1/2

Question 35

sin(pi/4)

Answer 35

(sq root 2)/2

Question 36

sin(pi/3)

Answer 36

(sq root 3)/2

Question 37

sin(pi/2)

Answer 37

1

Question 38

sin(pi)

Answer 38

0

Question 39

tan(0)

Answer 39

0

Question 40

tan(pi/6)

Answer 40

(sq root 3)/3

Question 41

tan(pi/4)

Answer 41

1

Question 42

tan(pi/3)

Answer 42

sq root 3

Question 43

tan(pi/2)

Answer 43

undefined

Question 44

tan(pi)

Answer 44

0

Question 45

graph y=x^2 - 2

Answer 45

parabola shifted down 2

Question 46

graph y= (x-3)^2

Answer 46

parabola shifted to the right 3

Question 47

trig integrals sincos

Answer 47

if sin power is odd use cos^2x= 1-sin^2x and make u=sinx

if cos power is odd use sin^2x= 1- cos^2x and make u=cosx

if they are both even use half angle identities

Question 48

trig identities tansec

Answer 48

if sec is even, use sec^2x=1+tan^2x and make u=tanx

if tan is odd, use tan^2x=sec^2x -1 and make u=secx

Question 49

trig sub

Answer 49

a2-x2 -> x=asin(theta)
a2+x2 -> x=atan(theta)
x2-a2 -> x=asec(theta)

Question 50

integral of 1/(x^2+a^2)

Answer 50

1/a • tan-1 (x/a) +C

Question 51

comparison theorem

Answer 51

f(x)>g(x)

if f(x) is convergent then g(x) is convergent

if g(x) is divergent then f(x) is divergent

Question 52

lim r^n

Answer 52

0 if -1

Question 53

geometric series

Answer 53

E ar^n-1

Question 54

geometric series sum

Answer 54

s=a/1-r and r<1, converges

diverges if r>or= 1

Question 55

if lim an

Answer 55

doesnt exist or doesnt equal 0, divergent

Question 56

arc length

Answer 56

L= integral of the sq. root (1+f’(x)^2)

Question 57

p-series

Answer 57

if p>1 convergent

if p<1 divergent