Calculus 2 Final | Actual Questions With Answers

1|Page


Calculus 2 Final | Actual Questions With
Answers


Direct Comparison Test-correct-answer-Given two series:
if "bigger" series converges, both converge
if "smaller" series diverges, both diverge




Limit Comparison Test-correct-answer-p = lim∞ A(k) / B(k)
if p is finite and p > 0, both series converge or diverge




Ratio Test-correct-answer-p = lim∞ [U(k+1) / U(k)]
p < 1, converges
p > 1, diverges
p = 1, inconclusive




Root Test-correct-answer-p = lim∞ U(k)∧(1/k)
p < 1, converges
p > 1, diverges
p = 1, inconclusive

, 2|Page




Alternating Series Test-correct-answer-converges if:
a) decreasing
b) lim∞ U(k) = 0 (pass divergence test)




Ratio Test for Absolute Convergence (RTAC)-correct-answer-p = lim∞ | U(k+1) /
U(k) |
p < 1, converges absolutely
p > 1, diverges
p = 1, inconclusive




MacLaurin Series-correct-answer-ƒ(0)+ƒ'(0)x+ƒ"(0)x²/2!+ƒ'''(0)x³/3!+.....
*(Taylor series centered at x = 0)




Taylor Series-correct-answer-ƒ(x₀)+ƒ'(x₀)(x-x₀)+ƒ"(x₀)(x-x₀)²/2!+ƒ'''(x₀)(x-x₀)³/3!+.....




Interval of Convergence-correct-answer-RTAC:
- p < 1, find interval