Final Prep

Question 1

What is the derivative of tanx

Answer 1

sec^2X

Question 2

What is the derivative of sinx

Answer 2

cosx

Question 3

What is the derivative of cosx

Answer 3

-sinx

Question 4

What is the integral of sec^2x

Answer 4

tanx

Question 5

What is the integral of sinx

Answer 5

-cosx

Question 6

What is the integration by parts formula

Answer 6

uv-integral(vdu)

Question 6

What is the integral of cosx

Answer 6

sinx

Question 7

In trigonometric integrals when the exponent of sin is odd and positive and the exponent of cos is a real number

Answer 7

split off a sinx and u = cosx

Question 8

In trigonometric integrals when the exponent of cos is odd and positive and the exponent of sin is a real number

Answer 8

split off a cosx and u = sinx

Question 9

sin^2x =

Answer 9

1 - cos^2x

Question 10

cos^2x =

Answer 10

1 - sin^2x

Question 11

Half angle formula for sin^2x

Answer 11

1/2(1-cos2x)

Question 12

In trigonometric integrals when the exponent of sin and cos are both even and non negative

Answer 12

Use the half angle formulas

Question 13

Half angle formula for cos^2x

Answer 13

1/2(1+cos2x)

Question 14

If an integral contains a^2 - x^2

Answer 14

x = asin(theta)

Question 15

If an integral contains a^2 + x^2

Answer 15

x = atan(theta)

Question 16

If an integral contains x^2 - a^2

Answer 16

x = asec(theta)

Question 17

Integral of a/x

Answer 17

a/dx ln(x) + C

Question 18

Formula for pumping problems

Answer 18

pg * Integral( D(y)*A(y) dy )

Question 19

Formula for lifting problems

Answer 19

pg * Integral( D(y) dy )

Question 20

Formula for spring problems

Answer 20

Integral( kx dx )

Question 21

In power series if the limit converges to 0

Answer 21

Radius is infinity and Interval of Convergence is negative infinity to positive infinity

Question 22

In a power series if the limit converges to infinity

Answer 22

Radius is zero and Interval of Convergence is a single point, the number that is being subtracted from x