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)]

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BC Calculus Review2

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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 25

Answers

1
What is g'(x) given g(x) = ∫f(t)dt from m(x) to n(x)
f(n'(x))-f(m'(x))
n'(x)×f(n(x))-m'(x)×f(m(x))
f(x)
f(n(x))-f(m(x))
2
Anti-derivative of cos(x)×tan(x)?
-cos(x)2/2 + c
DNE
-cos(x)
-cos(2x)/4 + c
3
Derivative of arccot(x):
1/(1+x2)
1/(1-x2)
1/√(1+x2)
-1/(1+x2)
4
Which of the following is false?
A=1/2×∫θ2 dθ
x=r×cos(θ)
r=c/(1+d×cos(θ))
y=r×sin(θ)
5
Which is false given Σa(k)ⁿ, n=0 to ∞?
The sum is a/(1-k).
The first term is a.
The series converges at |k|<1
The series converges at a=0.
6
dy/dy of a^x:
x×ax-1
ln(a)×ax
-ax
ax
7
Which is false given dP/dt = aP(b-P)?
a is the population at t=0
b is the carrying capacity
a is the logistic growth constant
dP/dt=0 as P→∞
8
Bonus: π/2-4/π×Σcos(x(2n-1))/(2n-1)²represents a repeating interval of what function?
Γ(x)
cos(x)×sin(x)
∫cos(x)×√(x) dx
|x|
9
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)
10
Euler's approximation states: f(x+a)=
f(x)×a+f(x)
f'(a)+f(x)
f'(x)×a+f(x)
f'(x)×a+f(a)
11
Derivative of A(t) = P(1+r/n)^nt:
r×t
r×P
r×A
rt
12
Derivative of arcsin(x):
1/(1+x2)
1/√(1-x2)
1/(x×√(x2-1))
1/√(x2-1)
13
Lagrange error states the error is less than:
Σfn+1(a)/(n+1)! × (x-a)
Σfn+1(a)/k! × (x-a)n+1
Σfn+1(a)/(n+1)! × (x-a)n+1
Σfn+1(a)/x! × (x-a)n+1
14
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) + ... + C
f'(x)×g''(x) - f''(x)×g'(x) + f'''(x)×g(x) - ... + C
15
Derivative of arcsec(x):
1/(√(1-x2))
1/(|x|×√(x2-1))
1/(x×√(1-x2))
1/(x×√(x2-1))
16
Arc length of f(x) is represented by:
∫√(x(t)2+y(t)2) dx
∫√(1+x(t)2) dx
∫√(x(t)2+y(x)2) dx
∫√(f(y)2+f(x)2) dx
17
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!-...
18
Anti-derivative of ln(x)/x:
1/2×ln(x)2 + c
1/x + c
ln(ln(x)) + c
ln(x)2 + c
19
Derivative of f(x) 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)]
[cos(θ)×r'(θ)]/[sin(θ)×r'(θ)]
[sin(θ)×r(θ)]/[cos(θ)×r(θ)]
20
Derivative of csc(x):
sec(x)2
sec(x)tan(x)
-csc(x)2
-csc(x)cot(x)
21
Anti-derivative of sec²(x):
tan(x)+c
ln(x)+c
1/3sec3(x)+c
csc(x)+c
22
Which does not equal cos(2x)?
cos(x)2(1-tan(x)2)
1-2sin(x)2
cos(x)2-sin(x)2
1-2cos(x)2
23
Find the function for the series: x+x³/3!+x⁵/5!
sin(x)
-sin(x)
ex
cos(x)
24
Σ 1/n^p converges for p is:
less than 0
greater than 0
equal to 0
greater than 1
25
Arc length of f(x) is represented by:
∫√(1+f(x)) dx
∫√(f(y)2+f(x)2) dx
∫√(1+f(x)2) dx
∫√(f(x)) dx

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