Calculus 2 Final Exam Review UPDATED ACTUAL Questions and CORRECT Answers

Calculus 2 Final Exam Review UPDATED
ACTUAL Questions and CORRECT
Answers
McLaurin Series for 1/(1-x) - CORRECT ANSWER - ∑xⁿ=1+x+x²+x³+x⁴+...

R=1



McLaurin Series for e^x - CORRECT ANSWER - ∑xⁿ/n!=1+x/1!+x²/2!+x³/3!+...

R=infinity



McLaurin Series for sinx - CORRECT ANSWER - ∑(-1)ⁿ(x²ⁿ⁺¹)/(2n+1)!=x-x³/3!+x⁵/5!-x⁷/7!+...

R=infinity



McLaurin Series for cosx - CORRECT ANSWER - ∑(-1)ⁿ(x²ⁿ)/(2n)!=1-x²/2!+x⁴/4!-x⁶/6!+...

R=infinity



Conditionally Convergent - CORRECT ANSWER - A series is ∑ a_n is called conditionally
convergent if it is convergent but not absolutely convergent.



Absolutely Convergent - CORRECT ANSWER - A series ∑ a_n is called Absolutely convergent if
the series of absolute values ∑ |a_n| is convergent


also if the series is absolutely convergent it is also convergent.



Root Test - CORRECT ANSWER - L=1 (nothing) L<1 (converges) L>1 (diverges)



Ratio Test - CORRECT ANSWER - L=1 (nothing) L<1 (converges) L>1 (diverges)



The Alternating Series Test - CORRECT ANSWER -

, Integral Test - CORRECT ANSWER -



Surface Area - CORRECT ANSWER -



Limit Laws for Sequences - CORRECT ANSWER -



Geometric Series - CORRECT ANSWER -



Divergence Test - CORRECT ANSWER -



P-Series Test - CORRECT ANSWER -



SA Rotation about x-axis - CORRECT ANSWER - f(x)



SA Rotating about y-axis - CORRECT ANSWER -x



Alternating Series Estimation - CORRECT ANSWER -



Integral Test Remainder Estimate - CORRECT ANSWER - For integral remainder 1/sqru(n^4+1) <
1/Sq(n^4) = 1/n^2
take integral of last one and b=inf and a=10



The Comparison Test - CORRECT ANSWER - (i) If ∑bn is convergent and an≤bn for all n, then ∑
an is also convergent.
(ii) If ∑bn is divergent and an≥bn for all n, then ∑ an is also divergent
.



practice prob - CORRECT ANSWER -