AP Calculus BC Study Guide UPDATED Exam Questions and CORRECT Answers

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AP Calculus BC Study Guide UPDATED Exam
Questions and CORRECT Answers✓
1/(1−x)

Ans:



1/(1+x)

Ans:



e^x

Ans:



sin(x)

Ans:



cos(x)

Ans:



ln(1+x)

Ans:



tan^-1(x)

Ans:



Converges by nth term test when

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,2


Ans: N/A



Diverges by nth term test when

Ans: lim an ≠ 0

n→∞



Converges by Geometric Series Test when

Ans: |r| < 1



Diverges by Geometric Series Test when

Ans: |r| > 1



Converges by p-series test when

Ans: p > 1



Diverges by p-series test when

Ans: p ≤ 1



Converges by Ratio test when

Ans: lim ( |an+1| / |an| ) < 1

n→∞



Diverges by Ratio test when




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,3


Ans: lim ( |an+1| / |an| ) > 1

n→∞



Converges by Direct Comparison test when

Ans: less than conv.



Diverges by direct comparison test when

Ans: greater than diver.



Converges by limit comparison when

Ans: lim ( |bn| / |an|) = +# & bn converges

n→∞



Diverges by limit comparison when

Ans: lim ( |bn| / |an| ) = +# & bn diverges

n→∞



Converges by Alternating series test when

Ans: lim an = 0 & an+1 < an

n→∞



Diverges by Alternating series test when

Ans: N/A



Converges by integral test when



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, 4


Ans: ∫conv. => ∑conv.



Diverges by integral test when

Ans: ∫div. => ∑div.



Sum of a geometric series

Ans: S = (a₁ / 1−r)



A=∫ 1/2 r² dθ

Ans: Area enclosed by a Polar equation



A=∫ ½ ((r_0)²-(r_1)²) dθ

Ans: Area between 2 polar curves



L=∫√(r²+(dr/dθ)²) dθ

Ans: Arc Length of a Polar Equation



A=∫ g(t) f'(t) dt

Ans: Area under a Parametric Curve



L= ∫√( (dx/dt)² + (dy/dt)²) dt

Ans: Arc Length of a Parametric Curve



(dy/dx)= (dy/dt)/(dx/dt) dx/dt≠0




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