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

Derivative of f(x) in terms of θ:

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

Given f(n)=g(m)=0, 1/(f(x)×g(x))

1/(g(n)×f(x)) + 1/(f(m)×g(x))

Which does not represent the derivative of f(x)/g(x)?

limh→0 [(f(x+h)-f(x)) /g(x)] / h

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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 36

Answers

1
Euler's approximation states: f(x+a)=
f'(x)×a+f(x)
f'(a)+f(x)
f'(x)×a+f(a)
f(x)×a+f(x)
2
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) + ... + 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
3
g(x) = ∫f(t)dt from 0 to x³. There is a point of inflection at
x=0
f(x)=0
f'(x)=0
g(x)=0
4
Lagrange error states the error is less than:
Σfn+1(a)/(n+1)! × (x-a)n+1
Σfn+1(a)/x! × (x-a)n+1
Σfn+1(a)/k! × (x-a)n+1
Σfn+1(a)/(n+1)! × (x-a)
5
Given r is the radius, r≠
x/cos(θ)
arctan(y/x)
√(x2+y2)
y/sin(θ)
6
Find the function for the series: x+x³/3!+x⁵/5!
-sin(x)
cos(x)
ex
sin(x)
7
Given z = r(cos(θ)+isin(θ)), zⁿequals
r(cos(nθ)+isin(nθ))
rn(cos(θ)+isin(θ))
rn(cos(θ)n+isin(θ)n)
rn(cos(nθ)+isin(nθ))
8
Σ 1/n^p converges for p is:
greater than 1
greater than 0
equal to 0
less than 0
9
Anti-derivative of sec²(x):
csc(x)+c
tan(x)+c
1/3sec3(x)+c
ln(x)+c
10
Bonus: π/2-4/π×Σcos(x(2n-1))/(2n-1)²represents a repeating interval of what function?
|x|
Γ(x)
∫cos(x)×√(x) dx
cos(x)×sin(x)
11
Derivative of arcsec(x):
1/(√(1-x2))
1/(|x|×√(x2-1))
1/(x×√(1-x2))
1/(x×√(x2-1))
12
Derivative of A(t) = P(1+r/n)^nt:
rt
r×t
r×A
r×P
13
Which of the following is false?
y=r×sin(θ)
r=c/(1+d×cos(θ))
A=1/2×∫θ2 dθ
x=r×cos(θ)
14
Anti-derivative of ln(x)/x:
ln(x)2 + c
ln(ln(x)) + c
1/x + c
1/2×ln(x)2 + c
15
∑(1+n)/n²diverges according to
Alternating series test
Direct comparison test
Limit comparison test
Ratio test
16
Which relationship is always true given f'(x) is never positive?
Σf(x) ≥ ∫f(x)
Σf(x) ≤ ∫f(x)
Σf(x) ≠ ∫f(x)
Σf(x) = ∫f(x)
17
Derivative of f(x) in terms of 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)]
[cos(θ)×r'(θ)-sin(θ)×r(θ)]/[sin(θ)×r'(θ)+cos(θ)×r(θ)]
18
Derivative of csc(x):
-csc(x)2
sec(x)tan(x)
-csc(x)cot(x)
sec(x)2
19
Arc length of f(x) is represented by:
∫√(1+f(x)) dx
∫√(1+f(x)2) dx
∫√(f(y)2+f(x)2) dx
∫√(f(x)) dx
20
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+...
21
You can take the derivative when there's a
vertical asymptote
cusp
horizontal asymptote
hole
22
Which is false given dP/dt = aP(b-P)?
a is the population at t=0
dP/dt=0 as P→∞
a is the logistic growth constant
b is the carrying capacity
23
What is g'(x) given g(x) = ∫f(t)dt from m(x) to n(x)
f(n'(x))-f(m'(x))
f(x)
f(n(x))-f(m(x))
n'(x)×f(n(x))-m'(x)×f(m(x))
24
Derivative of arccot(x):
1/√(1+x2)
-1/(1+x2)
1/(1+x2)
1/(1-x2)
25
dy/dy of a^x:
ax
ln(a)×ax
x×ax-1
-ax
26
Σf(n) is a converging series. Which can be f(n)?
1/(n+1)-1/(2-n)
1/n2
1/(n+1)+1/(n+2)
(1/(n+1)-1/(n+2))1/n
27
Given f(n)=g(m)=0, 1/(f(x)×g(x))
1/(g(n)×g(x)) + 1/(f(m)×f(x))
1/(g(m)×f(x)) + 1/(f(n)×g(x))
1/(f(n)×f(x)) + 1/(g(m)×g(x))
1/(g(n)×f(x)) + 1/(f(m)×g(x))
28
Which does not represent the derivative of f(x)/g(x)?
limh→0 [(f(x+h)-f(x)) /g(x)] / h
[g(x)×f'(x)-f(x)×g'(x)]/g2(x)
f(x)×g'(x)-1+g(x)×f'(x)-1
limh→0 [f(x+h) / g(x+h)-f(x)/g(x)] / h
29
If Σrⁿconverges Σrⁿ/n converges according to:
Direct comparison test
Ratio test
Limit comparison test
Alternating series test
30
Given g(a)=0 and f(a)=∞. Which limit can be found?
g(a)×f(a)
∞×g(a)
0×f(a)
g(a)/f(a)
31
Derivative of arcsin(x):
1/(x×√(x2-1))
1/(1+x2)
1/√(1-x2)
1/√(x2-1)
32
Given u=g(x), ∫f(g(x))×g'(x)dx =
∫f(u)dx
f(u)+c
∫f(u)×g'(x)du
F(g(x))+c
33
Which is false given Σa(k)ⁿ, n=0 to ∞?
The first term is a.
The series converges at a=0.
The sum is a/(1-k).
The series converges at |k|<1
34
Anti-derivative of cos(x)×tan(x)?
-cos(x)
-cos(2x)/4 + c
DNE
-cos(x)2/2 + c
35
Arc length of f(x) is represented by:
∫√(f(y)2+f(x)2) dx
∫√(x(t)2+y(t)2) dx
∫√(1+x(t)2) dx
∫√(x(t)2+y(x)2) dx
36
Which does not equal cos(2x)?
cos(x)2-sin(x)2
cos(x)2(1-tan(x)2)
1-2sin(x)2
1-2cos(x)2

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