Page | 1
AP Calculus BC Study Guide UPDATED
Exam Questions and Answers (Expert
Solutions)
Q: Converges by nth term test when, 🗹🗹: N/A
Q: Diverges by nth term test when, 🗹🗹: lim an ≠ 0
n→∞
Q: Converges by Geometric Series Test when, 🗹🗹: |r| < 1
Q: Diverges by Geometric Series Test when, 🗹🗹: |r| > 1
Q: Converges by p-series test when, 🗹🗹: p > 1
Q: Diverges by p-series test when, 🗹🗹: p ≤ 1
Q: Converges by Ratio test when, 🗹🗹: lim ( |an+1| / |an| ) < 1
n→∞
Q: Diverges by Ratio test when, 🗹🗹: lim ( |an+1| / |an| ) > 1
n→∞
Q: Converges by Direct Comparison test when, 🗹🗹: less than conv.
, Page | 2
Q: Diverges by direct comparison test when, 🗹🗹: greater than diver.
Q: Converges by limit comparison when, 🗹🗹: lim ( |bn| / |an|) = +# & bn converges
n→∞
Q: Diverges by limit comparison when, 🗹🗹: lim ( |bn| / |an| ) = +# & bn diverges
n→∞
Q: Converges by Alternating series test when, 🗹🗹: lim an = 0 & an+1 < an
n→∞
Q: Diverges by Alternating series test when, 🗹🗹: N/A
Q: Converges by integral test when, 🗹🗹: ∫conv. => ∑conv.
Q: Diverges by integral test when, 🗹🗹: ∫div. => ∑div.
Q: Sum of a geometric series, 🗹🗹: S = (a₁ / 1−r)
Q: A=∫ 1/2 r² dθ, 🗹🗹: Area enclosed by a Polar equation
Q: A=∫ ½ ((r_0)²-(r_1)²) dθ, 🗹🗹: Area between 2 polar curves
Q: L=∫√(r²+(dr/dθ)²) dθ, 🗹🗹: Arc Length of a Polar Equation
Q: A=∫ g(t) f'(t) dt, 🗹🗹: Area under a Parametric Curve
Q: L= ∫√( (dx/dt)² + (dy/dt)²) dt, 🗹🗹: Arc Length of a Parametric Curve
, Page | 3
Q: (dy/dx)= (dy/dt)/(dx/dt) dx/dt≠0, 🗹🗹: Derivative for Parametric Equations
Q: (d²y)/(dx²)=((d/dt)(dy/dx))/(dx/dt), 🗹🗹: Second derivative for Parametric
Equations
Q: x=f(t), 🗹🗹: x definition Parametric
Q: y=g(t), 🗹🗹: y definition Parametric
Q: x= r cos(θ), 🗹🗹: x definition Polar
Q: y= r sin(θ), 🗹🗹: y definition Polar
Q: θ=tan^-1(y/x), 🗹🗹: Cartesian to Polar conversion, Angle
Q: r=√(x²)+(y²), 🗹🗹: Cartesian to Polar conversion, Radius
Q: If P(t) = (x(t), y(t)), then dy/dx =, 🗹🗹:
Q: If P(t) = (x(t), y(t)), then d²y/dx² =, 🗹🗹:
Q: For the curve where P(t) = <x(t), y(t)>, the length of an arc =, 🗹🗹:
Q: If P(t) = <x(t), y(t)>, then then dP(t) =, 🗹🗹: <x'(t), y'(t)>
Q: For an object in motion along the curve P(t) = <x(t), y(t)>, the velocity vector for v(t)
is, 🗹🗹:
Q: For an object in motion along the curve P(t) = <x(t), y(t)>, the acceleration vector for
a(t) is, 🗹🗹:
AP Calculus BC Study Guide UPDATED
Exam Questions and Answers (Expert
Solutions)
Q: Converges by nth term test when, 🗹🗹: N/A
Q: Diverges by nth term test when, 🗹🗹: lim an ≠ 0
n→∞
Q: Converges by Geometric Series Test when, 🗹🗹: |r| < 1
Q: Diverges by Geometric Series Test when, 🗹🗹: |r| > 1
Q: Converges by p-series test when, 🗹🗹: p > 1
Q: Diverges by p-series test when, 🗹🗹: p ≤ 1
Q: Converges by Ratio test when, 🗹🗹: lim ( |an+1| / |an| ) < 1
n→∞
Q: Diverges by Ratio test when, 🗹🗹: lim ( |an+1| / |an| ) > 1
n→∞
Q: Converges by Direct Comparison test when, 🗹🗹: less than conv.
, Page | 2
Q: Diverges by direct comparison test when, 🗹🗹: greater than diver.
Q: Converges by limit comparison when, 🗹🗹: lim ( |bn| / |an|) = +# & bn converges
n→∞
Q: Diverges by limit comparison when, 🗹🗹: lim ( |bn| / |an| ) = +# & bn diverges
n→∞
Q: Converges by Alternating series test when, 🗹🗹: lim an = 0 & an+1 < an
n→∞
Q: Diverges by Alternating series test when, 🗹🗹: N/A
Q: Converges by integral test when, 🗹🗹: ∫conv. => ∑conv.
Q: Diverges by integral test when, 🗹🗹: ∫div. => ∑div.
Q: Sum of a geometric series, 🗹🗹: S = (a₁ / 1−r)
Q: A=∫ 1/2 r² dθ, 🗹🗹: Area enclosed by a Polar equation
Q: A=∫ ½ ((r_0)²-(r_1)²) dθ, 🗹🗹: Area between 2 polar curves
Q: L=∫√(r²+(dr/dθ)²) dθ, 🗹🗹: Arc Length of a Polar Equation
Q: A=∫ g(t) f'(t) dt, 🗹🗹: Area under a Parametric Curve
Q: L= ∫√( (dx/dt)² + (dy/dt)²) dt, 🗹🗹: Arc Length of a Parametric Curve
, Page | 3
Q: (dy/dx)= (dy/dt)/(dx/dt) dx/dt≠0, 🗹🗹: Derivative for Parametric Equations
Q: (d²y)/(dx²)=((d/dt)(dy/dx))/(dx/dt), 🗹🗹: Second derivative for Parametric
Equations
Q: x=f(t), 🗹🗹: x definition Parametric
Q: y=g(t), 🗹🗹: y definition Parametric
Q: x= r cos(θ), 🗹🗹: x definition Polar
Q: y= r sin(θ), 🗹🗹: y definition Polar
Q: θ=tan^-1(y/x), 🗹🗹: Cartesian to Polar conversion, Angle
Q: r=√(x²)+(y²), 🗹🗹: Cartesian to Polar conversion, Radius
Q: If P(t) = (x(t), y(t)), then dy/dx =, 🗹🗹:
Q: If P(t) = (x(t), y(t)), then d²y/dx² =, 🗹🗹:
Q: For the curve where P(t) = <x(t), y(t)>, the length of an arc =, 🗹🗹:
Q: If P(t) = <x(t), y(t)>, then then dP(t) =, 🗹🗹: <x'(t), y'(t)>
Q: For an object in motion along the curve P(t) = <x(t), y(t)>, the velocity vector for v(t)
is, 🗹🗹:
Q: For an object in motion along the curve P(t) = <x(t), y(t)>, the acceleration vector for
a(t) is, 🗹🗹:
