MATH 152 FINAL EXAM NAME

MATH152

FINAL EXAM

NAME

200 points

Mrs. BonnyTighe

Section 1. Find the derivative using logarithmic differentiation. ^ I x + l l a) .l\x):l ^l \x +t )

2. Evafuate: al

a da [csc3

Fri 5119106

b) J"-' sin2xdxclx-

3. Find the following limits.

b) liq(cosx)U'=

a)

( o2'\

l i m l. l ---\ x' /

lim .r2lnx =

4. Evaluate:

1

^

5. EvaluateLheintegralusingpartial fractions: l-: --J -4x: 'x--lx--J

6. Find the Macluarin seriesfor the given firnction andfind the radiusand interval of 1

convergence.f(x) = 4x+4

7. Determinewhetherthe seriesare convergentor divergentusingthe given test. lntegal Test ComparisonTest q\ $ sinn b) i-:-n hn ;,= Hn')+l

8. Find the radiusof convergenceandthe interval of convergenceif it is convergent.

f

H

5n X x + 1 )| ,"_ r r , , 1 . 4 ' 7 . . . (- 1 Qnn)nl

9. Expand ;--: (1-2x\"

asa powerseriesusingthebinomialseries. Statetheradiusof

convergence.

10.Setup but do not evaluatethe following: a) Findthelengthofthecurve,r =sect, ! =ln(l +l) ,0