AP Calculus BC: Series Tests, Trig Identities & Formulas
Studied by 6 people
Learn
Practice Test
Spaced Repetition
Match
Flashcards1/52
There's no tags or description
Looks like no tags are added yet.
Name | Mastery | Learn | Test | Matching | Spaced |
|---|
No study sessions yet.
53 Terms
sin2θ + cos2θ =
1
1 + tan2θ =
sec2θ
1 + cot2θ =
csc2θ
sin(2x) =
2sinxcosx
cos(2x) =
cos2x - sin2x
2cos2x-1
1-2sin2x
tan(2x) =
(2tanx) / (1-tan2x)
sin2x =
(1/2)(1-cos2x)
cos2x =
(1/2)(1+cos2x)
tan2x =
(1-cos2x) / (1+cos2x)
The arc length formula for a normal function is…?
∫ab√[ 1 + f’(x)2 ] dx
The derivative of a parametric function is…?
(dy/dt) / (dx/dt)
The second derivative of a parametric function is…?
(d/dt [dy/dx]) / (dx/dt)
Formula for the Arc Length of a parametric function:
∫ab√[ x’(t)2 + y’(t)2 ] dt
The vector function r’(t) =
<x’(t), y’(t)>
The vector function ∫abr(t) dt =
< ∫ab x(t) dt, ∫ab y(t) dt >
The polar function r(θ) =
y(θ) = rsinθ & x(θ) = rcosθ
The derivative of a polar function is…?
(dy/dθ) / (dx/dθ)
The formula for the area of a polar graph is…?
(1/2) ∫αβ r(θ)2 dθ
favg =
1/(b-a) * ∫ab f(x) dx
Formula for local linearization:
L(x) = f(x1) + f’(x1)(x-x1).
Integration by part formula:
∫udv = uv - ∫vdu
Logistic growth model formulas:
dP/dt = kP(1 - P/a)
dP/dt = kP(a - P)
When you know the formula of Sn, an = …?
Sn - Sn-1
The infinite sum of a geometric series is…?
a / (1-r), where |r| < 1
The range of the error bound is…?
0 < Rn < an+1 OR an+1 < Rn < 0
Taylor polynomial formula:
(1/n!) (f(n)(c)) (x-c)n
Lagrange Error Bound:
|Error| <= M|x-c|n+1/ (n+1)!
M in the Lagrange Error bound is equal to…?
M >= |fn+1(z)|
M in the Lagrange Error Bound represent…?
the y-value that has the greatest absolute value.
The interval of convergence is…?
the range of x values that will result in the power series to converge.
The radius of convergence is…?
how far away you can go from the center point and still make the power series converge.
The power series of ex is…?
∑∞n=0 xn / n!
The power series for sinx is…?
∑∞n=0 (-1)n(x2n+1) / (2n+1)!
The power series of cosx is…?
∑∞n=0 (-1)n(x2n) / (2n)!
Divergence Test
If limx→∞ an doesn’t equal 0, the series ∑∞n=1 an will converge.
Integral Test
If f(x) is always positive, continuous, and decreasing on the interval [k, ∞), then if ∫k∞ f(x) dx is convergent, the series ∑∞n=1 f(n) will converge.
P-series test
When you have a series like ∑∞n=1 1/np, if p > 1, the series converges.
Comparison Test
Given ∑∞n=1 an , ∑∞n=1 bn , an and bn >= 0 for every value, & an <= bn. If ∑∞n=1 bn converges, so does ∑∞n=1 an. If ∑∞n=1 an diverges, so does ∑∞n=1 bn.
Limit Comparison Test
Given ∑∞n=1 an , ∑∞n=1 bn , & an and bn >= 0 for every value. If limx→∞ an / bn is positive and finite, either both converge or diverge.
Alternating Series Test
Given ∑∞n=1 (-1)n an & an >= 0 for all values of n, if limx→∞ bn = 0 & bn is a decreasing sequence, ∑∞n=1 (-1)n an converges.
Ratio Test
Given ∑∞n=1 an & limx→∞ an = L, if L is < 1 the series converges. If L = 0, it is inconclusive. If L > 1, the series diverges.
A series converges absolutely if…?
the series converges in its original form and its absolute value form.
A series converges conditionally if…?
the series only converges in its original form.
Surface Area of cube
6s2
Volume of cube
s3
Surface area of rectangular prism
2(lw + lh + wh)
Volume of rectangular prism
lwh
Volume of cones & pyramids
(1/3)Bh
Surface Area of cone
πrs + πr2
Surface Area of cylinder
2πr + 2πr2
Surface Area of sphere
4πr2
Volume of sphere
(4/3)πr3
Note 
Flashcards (122)