Final Exam

Question 1

d/dx sinx

Answer 1

cosx

Question 2

d/dx cosx

Answer 2

-sinx

Question 3

d/dx tanx

Answer 3

sec^2x

Question 4

d/dx cotx

Answer 4

-csc^2x

Question 5

d/dx secx

Answer 5

tanxsecx

Question 6

d/dx cscx

Answer 6

-cscxcotx

Question 7

d/dx arcsinx

Answer 7

1/sqrt(1-x^2)

Question 8

d/dx arccosx

Answer 8

-1/sqrt(1-x^2)

Question 9

d/dx arctanx

Answer 9

1/(1+x^2)

Question 10

d/dx arccotx

Answer 10

-1/(1+x^2)

Question 11

d/dx arcsecx

Answer 11

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

Question 12

d/dx arccscx

Answer 12

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

Question 13

d/dx sinhx

Answer 13

coshx

Question 14

d/dx coshx

Answer 14

sinhx

Question 15

d/dx tanhx

Answer 15

sech^2x

Question 16

d/dx cothx

Answer 16

-csch^2x

Question 17

d/dx sechx

Answer 17

-sechxtanhx

Question 18

d/dx cschx

Answer 18

-cschxcothx

Question 19

d/dx arcsinhx

Answer 19

1/sqrt(x^2+1)

Question 20

d/dx arccoshx

Answer 20

1/sqrt(x^2-1)

Question 21

d/dx arctanhx

Answer 21

1/(1-x^2)

Question 22

d/dx arccothx

Answer 22

1/(1-x^2)

Question 23

d/dx arcsechx

Answer 23

-1/xsqrt(1-x^2)

Question 24

d/dx arccschx

Answer 24

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

Question 25

Arc Length Formula

Answer 25

ds = sqrt(1+(dy/dx)^2)dx

Question 26

Simpsons Rule Formula

Answer 26

Δx/3*(y0+4y1+2y2+4y3+4y4+2y5+4yn-1+yn)

Question 27

Disk Method around x-axis Formula

Answer 27

V = π∫(y^2)dx

Question 28

Disk Method around y-axis Formula

Answer 28

V = π∫(x^2)dx

Question 29

Shell Method around a Vertical Line

Answer 29

V = 2π∫xf(x)dx

Question 30

Shell Method around a Horizontal Line

Answer 30

V = 2π∫yf(y)dx

Question 31

Surface Integral around x-axis

Answer 31

S = 2π∫ysqrt(1+y’^2)dx

Question 32

Surface Integral around y-axis

Answer 32

S = 2π∫xsqrt(1+x’^2)dx

Question 33

Geometric Series Convergence Formula

Answer 33

r*(1/(1-r))

Question 34

Taylor Series Coefficient Formula

Answer 34

f^(n)(x)/n!