What pattern does the tabular method follow given ∫ f(x) × g''(x) dx?

f(x)×g'(x) - f'(x)×g(x) + f''(x)×G(x) - ... + C

The slope of the tangent line in terms of θ:

[cos(θ)×r'(θ)-sin(θ)×r(θ)]/[sin(θ)×r'(θ)+cos(θ)×r(θ)]

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AP Calculus BC Review

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This is a review of the basic formulas learned in BC calculus. Warning: all derivatives that should be memorized give you 5 seconds to answer. #math #calculus #formulas

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Questions 22

Answers

1
Σ 1/n^p converges for p is:
equal to 0
greater than 1
greater than 0
less than 0
2
Which is false given dP/dt = aP(b-P)?
a is the population at t=0
dP/dt=0 as P→∞
b is the carrying capacity
a is the logistic growth constant
3
Anti-derivative of cos(x)×tan(x)?
-cos(x) + c
DNE
-cos(x)2/2 + c
-cos(2x)/4 + c
4
Which of the following is false?
y=r×sin(θ)
r2=x2 + y2
A=1/2×∫θ2 dθ
x=r×cos(θ)
5
Find the function for the series: x-x³/3!+x⁵/5!-...
-sin(x)
cos(x)
sin(x)
ex
6
Derivative of arcsin(x):
1/√(x2-1)
1/(1+x2)
1/√(1-x2)
1/(x×√(x2-1))
7
Arc length of f(x) is represented by:
∫√(1+f'(x)2) dx
∫√(f'(x)) dx
∫√(1+f'(x)) dx
∫√(f(y)2+f(x)2) dx
8
Derivative of csc(x):
sec(x)tan(x)
-csc(x)cot(x)
sec(x)2
-csc(x)2
9
Euler's approximation states: f(x+a)=
f '(x)×a+f(x)
f '(x)×a+f(a)
f '(a)+f(x)
f(x)×a+f(x)
10
What pattern does the tabular method follow given ∫ f(x) × g''(x) dx?
f''(x)×g'(x) - f'''(x)×g(x) + ... + C
f(x)×g'(x) - f'(x)×g(x) + f''(x)×G(x) - ... + C
f'(x)×g''(x) - f''(x)×g'(x) + f'''(x)×g(x) - ... + C
f'(x)×g(x) - f''(x)×G(x) + ... + C
11
Arc length of f(x) is represented by:
∫√((f'(y))2+(f'(x))2) dx
∫√(x'(t)2+y'(x)2) dx
∫√(1+x(t)2) dx
∫√((x'(t))2+(y'(t))2) dt
12
The slope of the tangent line in terms of θ:
[cos(θ)×r'(θ)+sin(θ)×r(θ)]/[sin(θ)×r'(θ)+cos(θ)×r(θ)]
[cos(θ)×r'(θ)-sin(θ)×r(θ)]/[sin(θ)×r'(θ)+cos(θ)×r(θ)]
[sin(θ)×r(θ)]/[cos(θ)×r(θ)]
[cos(θ)×r'(θ)]/[sin(θ)×r'(θ)]
13
Derivative of arcsec(x):
1/(x×√(1-x2))
1/(√(1-x2))
1/(x×√(x2-1))
1/(|x|×√(x2-1))
14
Bonus: π/2-4/π×Σcos(x(2n-1))/(2n-1)²represents a repeating interval of what function?
∫cos(x)×√(x) dx
Γ(x)
cos(x)×sin(x)
|x|
15
Which does not equal cos(2x)?
cos(x)2-sin(x)2
1-2sin(x)2
1-2cos(x)2
cos(x)2(1-tan(x)2)
16
Taylor series for ln(x+1):
x-x2/2!+x3/3!-...
-x-x2/2-x3/3-...
x+x2/2+x3/3+...
x-x2/2+x3/3-...
17
Lagrange error states the error is less than:
fn+1(z)/k! × (x-a)n+1
fn+1(z)/(n+1)! × (x-a)
fn+1(z)/(n+1)! × (x-a)n+1
fn+1(z)/x! × (x-a)n+1
18
What is g'(x) given g(x) = ∫f(t)dt from m(x) to n(x)
f(n'(x))-f(m'(x))
f(n(x))-f(m(x))
f(x)
n'(x)×f(n(x))-m'(x)×f(m(x))
19
Derivative of arccot(x):
1/√(1+x2)
1/(1+x2)
-1/(1+x2)
1/(1-x2)
20
Anti-derivative of sec²(x):
1/3sec3(x)+c
ln(x)+c
tan(x)+c
csc(x)+c
21
Which is false given Σa(k)ⁿ, n=0 to ∞?
The sum is a/(1-k).
The series converges at |k|<1
The series converges at a=0.
The first term is a.
22
Anti-derivative of ln(x)/x:
1/x + c
1/2×ln(x)2 + c
ln(x)2 + c
ln(ln(x)) + c

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