Final Review

Question 1

derivative of f(x)/g(x)

Answer 1

[g(x)f’(x) - f(x)g’(x)]/(g(x)^2)

Question 2

derivative sin(x)

Answer 2

cos(x)

Question 3

derivative tan(x)

Answer 3

sec^2(x)

Question 4

derivative cos(x)

Answer 4

-sin(x)

Question 5

derivative sec(x)

Answer 5

sec(x)*tan(x)

Question 6

derivative cot(x)

Answer 6

-csc(x)

Question 7

integral of -csc(x)*cot(x)

Answer 7

csc(x)

Question 8

integral of 1/sqrt(1-x^2)

Answer 8

arcsin(x)

Question 9

integral of 1/1+x^2

Answer 9

arctan(x)

Question 10

integral of 1/abs(x)*sqrt(x^2-1)

Answer 10

arcsec(x)

Question 11

integral of b^x

Answer 11

b^x/ln(b)

Question 12

integral of ln (x)

Answer 12

x * ln(x) - x

Question 13

trig identity with cos and sin squared

Answer 13

sin^2 + cos^2 = 1

Question 14

trig identity that equals sec^2

Answer 14

1 + tan^2

Question 15

trig identity that equals csc^2

Answer 15

1+cot^2

Question 16

MacLaurin for 1/1-x

Answer 16

x^n

Question 17

MacLaurin for e^x

Answer 17

x^n/n!

Question 18

MacLaurin for sin(x)

Answer 18

-1^n (x^(2n+1) / (2n+1)!)

Question 19

MacLaurin for cos(x)

Answer 19

-1^n (x^2n / (2n+1)!)

Question 20

MacLaurin for ln(1+x)

Answer 20

-1^(n+1) x^n/n

Question 21

MacLaurin of arctan(x)

Answer 21

-1^n (x^(2n+1) / 2n+1)

Question 22

MacLaurin of (1+x)^r

Answer 22

(r n) x^n

Question 23

integral of -1/sqrt (1-x^2)

Answer 23

-1/sqrt (1-x^2)arccos(x)

Question 24

integral of -1/1+x^2

Answer 24

arccot(x)

Question 25

integral of -1/ abs(x)* sqrt(x^2-1)

Answer 25

arccsc(x)

Question 26

integral of tan(x)

Answer 26

-ln |cos(x)|

Question 27

integral of sec(x)

Answer 27

ln |sec(x)+tan(x)|

Question 28

trig identity for sin^2(x)

Answer 28

1/2 - cos(2x)

Question 29

formula for Taylor series

Answer 29

f^(n)(a) / n! * (x-a)^n

Question 30

to convert polar to cartesian

Answer 30

x = r * cos(x)
y = r * sin(x)

Question 31

to convert cartesian to polar

Answer 31

r = sqrt ( x^2 + y^2 ) 
theta = arctan ( y/x )
r^2 = x^2 + y^2