midterm memorization

Question 1

d/dx sin(x)

Answer 1

cos(x)

Question 2

d/dx cos(x)

Answer 2

-sin(x)

Question 3

d/dx tan(x)

Answer 3

sec²(x)

Question 4

d/dx cot(x)

Answer 4

-csc²(x)

Question 5

d/dx sec(x)

Answer 5

sec(x)tan(x)

Question 6

d/dx csc(x)

Answer 6

-csc(x)cot(x)

Question 7

d/dx arcsin(x)

Answer 7

1/√(1-x²)

Question 8

d/dx arccos

Answer 8

-1/√(1-x²)

Question 9

d/dx arctan(x)

Answer 9

1/1+x²

Question 10

d/dx arccsc(x)

Answer 10

-1/ x* √(x²-1)

Question 11

d/dx arcsec(x)

Answer 11

1/x* √(1-x²)

Question 12

d/dx arccot(x)

Answer 12

-1/1+x²

Question 13

what is the trig substitution for sqrt(1-x²)?

Answer 13

x =asinθ
cos² θ= 1- sin²θ

Question 14

what is the trig substitution for sqrt(x²-1)?

Answer 14

x=asecθ
tan²θ = sec²θ -1

Question 15

what is the trig substitution for sqrt(1+x²)?

Answer 15

x = atanθ
sec²θ = 1+ tan²θ

Question 16

what is the trig identities?

Answer 16

sin²x + cos²x= 1
tan²x + 1 = sec²x
1 + cot²x = csc²x

Question 17

what are the double angle formulas?

Answer 17

sin(2θ) = 2sinθcosθ
cos(2θ) = cos²θsin²θ
= 2cos²θ - 1
= 1 - 2sin²θ

Question 18

what is the cos²x and sin²x identity?

Answer 18

cos²x = (1+cos2x)/2
sin²x = (1-cos2x)/2

Question 19

equation to find the slope (first derivative) of a parametric curve

Answer 19

(dy/dt)/(dx/dt)

Question 20

equation to find the second derivative of a parametric curve

Answer 20

d²y/dx² = d/dx (dy/dx) = d/dt (dy/dx)/ dx/dt

Question 21

equation to find the area of a parametric curve

Answer 21

A=∫βα ydx = ∫t0t1 g(t)f’(t)dt

Question 22

equation to find the arc length of a parametric curve

Answer 22

L=∫βα √((dx/dt)²+(dydt)²)dt

Question 23

what is the integral of tan(x)

Answer 23

ln|sec(x)|+ C

Question 24

what is the integral of sec(x)

Answer 24

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

Question 25

what is the integral of 1/ax+b?

Answer 25

1/a*ln|ax+b|