CALCULUS II FINAL EXAM REVIEW WITH ANSWERS #13 2025-26
Divergence Test - correct answer If the limit of a[n] is not zero, or does not exist, then
the sum diverges.
Integral Test - correct answer Where f(x) continuous, positive, decreasing over [1, ∞)
and an=f(n), if 1∫∞f(x) convergent, Σan convergent. If 1∫∞f(x) divergent, Σan divergent.
Comparison Test - correct answer Find Bn>An if it converges then An converges.
Find Bn<An if it diverges An diverges.
Limit Comparison Test - correct answer if lim as n approaches ∞ of ratio of comparison
series/general term is positive and finite, then series behaves like comparison series
Alternating Series Test - correct answer lim as n approaches zero of general term = 0
and terms decrease, series converges
Ratio Test - correct answer r<1 converges
R> diverges
R=1 inconclusive
Geometric Series - correct answer ar^n
Converge if abs(r) < 1
Diverge if abs(r) >= 1
P-series - correct answer 1/(n^p)
If p > 1, Converges
If p <= 1, Diverges
Absolute Convergence - correct answer If the absolute value of the series converges,
the series converges
Taylor Series - correct answer f(c)+f'(c)(x-c)+f''(c)(x-c)^2/2 ... +f^n(c)(x-c)^n/n!
Interval of Convergence for Power Series - correct answer
Partial sum - correct answer the sum of the first n terms of a series
Telescoping Series - correct answer A series whose partial sums eventually only have a
fixed number of terms after cancellation
Area of a Surface of Revolution - correct answer double integral of sqrt (1 + (dz/dx)^2 +
(dz/dy)^2) da
Divergence Test - correct answer If the limit of a[n] is not zero, or does not exist, then
the sum diverges.
Integral Test - correct answer Where f(x) continuous, positive, decreasing over [1, ∞)
and an=f(n), if 1∫∞f(x) convergent, Σan convergent. If 1∫∞f(x) divergent, Σan divergent.
Comparison Test - correct answer Find Bn>An if it converges then An converges.
Find Bn<An if it diverges An diverges.
Limit Comparison Test - correct answer if lim as n approaches ∞ of ratio of comparison
series/general term is positive and finite, then series behaves like comparison series
Alternating Series Test - correct answer lim as n approaches zero of general term = 0
and terms decrease, series converges
Ratio Test - correct answer r<1 converges
R> diverges
R=1 inconclusive
Geometric Series - correct answer ar^n
Converge if abs(r) < 1
Diverge if abs(r) >= 1
P-series - correct answer 1/(n^p)
If p > 1, Converges
If p <= 1, Diverges
Absolute Convergence - correct answer If the absolute value of the series converges,
the series converges
Taylor Series - correct answer f(c)+f'(c)(x-c)+f''(c)(x-c)^2/2 ... +f^n(c)(x-c)^n/n!
Interval of Convergence for Power Series - correct answer
Partial sum - correct answer the sum of the first n terms of a series
Telescoping Series - correct answer A series whose partial sums eventually only have a
fixed number of terms after cancellation
Area of a Surface of Revolution - correct answer double integral of sqrt (1 + (dz/dx)^2 +
(dz/dy)^2) da
