This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: ; 408 D (Test 1) . ‘ Fall'07 (Version B) Erma 39w?” éCSwﬁJJm SMQEJAW‘M @100 {2Q Name Make swam“ have , , L v P nun—>00 " IfLim 1’"—”—exists and is greater than 1 (or inﬁnite), the series diverges. n—wo’ p" Show all work: gm“? Te»
ﬂ .‘ 1
{im ham 1 ’x {ﬁtsbx _ 1 12+ p2 + ....+pn + be a series ofpositive terms.
Vaﬂfum PM exists and is less than 1; converges. Cxé’weiré [AD/’7 V‘ng ff;
/ fiar‘zwgr ua flair: g
Z i
Z
i J a? (3L: axe/m cam OE, M408DTest1Fall’06pg2bfnb 2) a. Determine whether the series is converge or divergent.
If it is convergent, ﬁnd its sum. Show all work. (8 pt (2)“ + 6.33
iﬁﬁnLﬁiﬁaf/é) L: o  ft 73 “f 3mm“ w/ 1*: 5/2; Ag M408DTest1Fall’07pg3bfnb l 3) Use the integral test to determine whether'the
series is convergent or divergent. (10 pts)
Show all work. Make sure you can use the integral test. 0° 3
n w I x f} 3
— W7) Inf}: é
en . >< y:
t 11:1 ﬂ~?5‘0 g j" . n
5 .3 x
63;" X 5 "312 z’: X“ e“ 1:555?» ‘5 W m if: l
w . t: a
» “ex. 3 x r l
5" " ,1“ m r; 2 m r: , m r: v I V) “" G”; if V} a“ .21?” f: "“r
.. G x .1 / w i a i m :5 ’0 7pg4bfnb 4) Determine whether the series converges orvdiverges. (10 pts)
°° sin2(n) n2+1 éirﬁqu); 5— ! ! M4 08DTest1Fall ’07pg5bf nb \ 3 i i ‘i ‘3 ‘i' E? m 47% V
5)ShowthatT13+il3—+3i3—f;+3%+g;+m
(three positive terms alternating with one L3,) > 50+: negative term) converges. Mar/mm ‘ ééﬂ‘éﬁ 75' M408DTeSt1Fall’07pg6bfnb 1 6) How many terms of the series do we need "to add > in order to ﬁnd the sum to the indicated accuracy? oo (_ 1 )n+l I  v , lerrorl < 0.001 ‘5’ Ema» n3 3! j 408DTest1Fall’07pg7bfnb 7) A car is moving with speed 21 m/s, acceleration
1 m/szand jerk .05 m/s3 at a given instant. Using a third degree Taylor polynomial, estimate
how far the car moves in the next second. gigs} * a: {£3} 3 ire/5:“
' i 3 g m; (m a» _ W f~ " "
lg {a} r: 2! + f: T b (090'
(> = mom +9300 +53  mmwxmmatbnwwv M4 08DTestI Fall ’0 7pg8bf nb 8) Find the radius of convergence and the interval
of convergence for the series. I °° (7x—3)” M4 08DTest1 F all ’0 7 pg9b f nb 9) Find a power series representation for the function
and determine the interval of convergence. .. i _ V ,g EWMW {€M(XL\5EI ‘ E5" ,f’ ,1 ‘ i M408DTest1Fall'07pg10bfnb 10) Approximate f by a Taylor polynomial with degree n at a.
f(x)=exz, c220, 1122, 05x:0.1 :3 o5  ,3; ll feagvfamrm Use Taylor's Inequality to estimate the accuracy of the approximation
of T 2(x) to f (x). ...
View
Full Document
 Spring '07
 Sadler
 Calculus, Power Series, Taylor Series, Mathematical Series, series ofpositive terms

Click to edit the document details