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Unformatted text preview: M ath 242 Section 050: Test #3
NAME: „ _____ There are 6 questions on 6 pages. P ointy per page: 5, 5, 5, 0, 5, 6.
The 7th page has some f ormulas you can refer to if needed.
[5 points] Question 1. D etermine whether the i nfinite series is absolutely convergent, conditionally convergent, or divergent.  \.<l
Tf
Jt  " I/O [5 points] Question 2. F ind t he interval of convergence of t he power ^ ' 3??, an =  as 9 < 5" ? or < [5 p ointy] Question 3. Find a power series r epresentation of the f unction
l+4xlx'
Then use the f irst t hree terms of t hai, series (the constant term, the x t erm,
,,
9
r!
1 004
and the x t erm to imd an a pproximation to .
;
0.999 /)lso l'X 0(^0.001 ^ 1 +0.00^ ^ i± 0.005 +0.000005
L'°'ooi ~ [6 points] Question 4. Find the first t hree t erms of t he Taylor series for t he
function
/(*) = ( !+a:) 1 / 2
and use those first three terms to get an approximation for (1.08)1/2. o " ^
' i L+. 2. [5 points] Question 5. Find t he f irst t hree terms of the Taylor series for the
function
f ( x ) =e. x sin(x). 11 3! 2\L 5. 7
35" 3
*_ Y
*3 (o  ^y^
3
z — s [6 points] Question 6. Consider the p arametric curve x — t + \u t, y — t — ln /,,
whore 0 < t < oo. F ind dy/dx jiiid d2y/dx2. F ind where the curve is
increasing, decreasing, concave up, or concave down. Sketch the curve. / •t /)< ;f i<l d
d tfl
A\WMjS C$f\cd\fc uf> ...
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 Spring '08
 wang

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