For Final

Question 1

Quadratic Formula

Answer 1

to find roots of a quadratic equation

x = -b +/- √(b2-4ac)
2a

Question 2

Fundamental Trig Identities (1)

Answer 2

cscθ = 1/sinθ
secθ = 1/cosθ
tanθ = sinθ/cosθ
cotθ = cosθ/sinθ

Question 3

Fundamental Trig Identities (2)

Answer 3

sin2θ + cos2θ = 1
1 + tan2θ = sec2θ
1 + cot2θ = csc2θ

Question 4

Fundamental Trig Identities (3)

Answer 4

sin(-θ) = -sin(θ)
cos(-θ) = cos(θ)
tan(-θ) = -tan(θ)

Question 5

Fundamental Trig Identities (4)

Answer 5

sin(π/2 - θ) = cosθ
cos(π/2 - θ) = sinθ
tan(π/2 - θ) = cotθ

Question 6

Addition and Subtraction Formulas

Answer 6

sin(x+y) = sinx*cosy + cosx*siny
sin(x-y) = sinx*cosy - cosx*siny
cos(x+y) = cosx*cosy - sinx*siny
cos(x-y) = cosx*cosy + sinx*siny
tan(x+y) = (tanx + tany) / (1 - tanx*tany)
tan(x-y) = (tanx - tany) / (1 + tanx*tany)

Question 7

Double-Angle Formulas

Answer 7

sin2x = 2sinx*cosx
cos2x = cos2x - sin2x = 2cos2x - 1 = 1 - 2sin2x
tan2x = (2tanx) / (1 - tan2x)

Question 8

Half-Angle Formulas

Answer 8

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

Question 9

Trig Function Derivatives

Answer 9

cos(x) = -sin(x)
sin(x) = cos(x)
tan(x) = sec2(x)
cot(x) = -csc2(x)
sec(x) = sec(x)*tan(x)
csc(x) = -csc(x)*cot(x)

Question 10

Basic Integration Formulas

Answer 10

d/dx (C) = 0 ∫ 0 dx = C
d/dx (xn) = nxn-1 ∫ xn dx = (xn+1)/(n+1) + C
d/dx (lnx) = 1/x ∫ 1/x dx = lnx + C
d/dx ax = axlna ∫ ax dx = ax/lna + C

Question 11

Three ways a Limit fails to exist:

Answer 11

You approach two different Y-values as X approaches the given value from the right and from the left
Unbounded behavior from the function in either (or both) direction
Oscillating Behavior

Question 12

Two Special Limits

Answer 12

limx->0(sin(x)) / x = 1

limx->0(cos(x)) - 1 / x = 0

Question 13

A function is continuous if…:

Answer 13

The limit of f(x) at x = a exists
limx->a f(x) exists
The function must exist
f(a) exists
the limit and the function must be equal
limx->a f(x) = f(a)

Question 14

How to know you have a horizontal asymptote

Answer 14

If you start with infinity and end with a finite number, you have a horizontal asymptote.

Question 15

How to know you have a vertical asymptote

Answer 15

If you start with a finite value and end with infinity, you have a vertical asymptote.

Question 16

Derivatives:

Quotient Rule

Answer 16

f(x) = (lowDhigh) - (highDlow) / (denominaator)2

Question 17

Derivatives:

Product Rule

Answer 17

f(x) = 1stD2nd + 2ndD1st

Question 18

Inverse Trig Function Derivatives

Answer 18

d/dx [sin-1x] = 1 / (√1 - x2)
d/dx [cos-1x] = -1 / (√1 - x2)
d/dx [tan-1x] = 1 / (1 + x2)
d/dx [cot-1x] = -1 / (1 + x2)
d/dx [sec-1x] = 1 / |x|(√x2 - 1)
d/dx [csc-1x] = -1 / |x|(√x2 - 1)

Question 19

Derivatives:

Natural Log

Answer 19

lnx = 1 ‘nover’ x

d/dx [lnx] = 1/x

Question 20

Where do you look for critical numbers?

Answer 20

Where the derivative Does Not Exist and where the derivative equals Zero

Question 21

Rolle’s Theorum

Answer 21

f(x) is continuous on [a,b]
f(x) is differentiable on (a,b)
f(a) = f(b)
Conclusion: There is at least one value of C in (a,b) such that f’(c) = 0

Question 22

Mean Value Theorum

Answer 22

f(x) is continuous on [a,b]
f(x) is differentiable on (a,b)
Conclusion: There is at least one C in (a,b) such that f’(c) = (f(b) - f(a)) / (b - a)