University:
Amherst College
Course:
MATH 106 | Calculus with Elementary Functions
Academic year:

2017
Views:

63

Pages:

8
Author:

unentafq3

Name:. kCAL7 College DEPARTMENT OF MATHEMATICS Math 106 Midterm Exam # 3 April 19 , 2017 • This is a closed-book examination. No books, notes, calculators, cell phones, communication of any devices sort , webpages, or other aids are permitted. •Simplify numerical answers such as sin , ln(e3), e21n 3 and 4§. • Please show all of your work and justify all of your answers. (You may use the backs of pages for additional work space.) Problem Score Possible Points 1 30 2 10 3 54 4 6 Total 100 1. [30 Points] Compute each of the following derivatives. (a) y' where y = ^ s» w\ pl » ivj ^ SIlA y = zJL ^ ==?u3' 3- ' &>3X 4- rlwx ( b) Sd " / (sin2 x ) \/ l + sec ^ / x ( 5 - x7 ) 2 e — cos I ^ (^ Iv\x ) • -- -2 + I J- Do not simplify your fined answer here. . • ^ (s -x7) -h ' _ I ^ ( tanx ) j \ - *) aVv 5 -W ) U juflW * ] Ly ^ */ ^ ( 4 JK . ix 5 x J- 1K ^ O-A In vl + sec5 ^ -1 - 1 t rsec lx + V,2- ' c (5 " ^ IK ) + .5 & Z slSx* 2 . 6^VA"K \AV^C ^ 0 a ' + 2. • SlL 2 * — 1 -feet 2 X 2 ) " 2^C.6 X * Se xr feiv'v ^ ' ^ 2. (10 Points] Find the equation of the tangent line to the curve = y r ln ( l + cosx ) + cos ( ln( l 4 x )) - eainz * - l + ln(x 4 l) + \1ex+1 cos( ea: at the point where x = 0. y W iy£scT) )) - Ze. VosWct-Ms c : (j-$\wx) y'" [\ ) - c -^X l +X |4 e "jVhJUlx+ o] ^ •« * X-H WviU !< Cov\ - \ ) * { e * e * ) \ (x) ± e * G * p/oJUc7i~ /v4e / 51ofe- : ^ -O O o I ^ 0 -hO ^^ ?dv 0 - -t- 0 4-6 — -Z& ~ |( X - - X + 2£ , r . O) " 3 3. [54 Points] Evaluate each of the following integrals. Simplify. rjUz- c x r* V -Y+ c f0 -\-_£ (. 0 I o ^ a- 3e3 — ~> — « ~ Z- Wc^l 0 wj14? r " 0^ 2- -P ^- 2 e* 6* e/ ' + IA XX a\x — > a.> - 2 ov - 2 " 3 MJ*) 4 / ' - JU (J i-2 -J^ <5zV = 3. ( Continued ) Evaluate each of the following integrals. Simplify. 3 \/4 — In x x dx ^ '" I 'X 2 M 3 ^ _ X -2 . 3 sj 3 x= l =$ x = e> # (d ) / / I “ — 1 - X2 SPLIT -t dx -e = jLlx| ed '4 I i 2, + —_ Z 2 - ^ Zr A Ac ~ z. 3 3 \ >4 __ - / 1U\X L /_ 3 z. 5 3. ( Continued ) Evaluate each of the following integrals. Simplify. (sf - l) (s 3 (e ) (f ) / - X* k VieHVl ' ) X */ •* ^ 2- 31 e du. - 2 >C z- An ^ zix cU * 2 w - t+4T - 2. ^- 2c _< 3 3. ( Continued ) Evaluate the following integral. Simplify. rE % * tan (3 ) dx r: x ( g) JO I r " U-CQ5C3 X) I " du ' / 3 " 3>sK(.3x) s 0 4. [6 Points] Find the function f ( x ) that satsifies f' ( x ) ~ J — 3e -e5 ^ 11 3 e/- 65 cU ^ 3> e/* dx ^ ^ = i / (5) ss 2. _ 3 e* LIU -K. = 1 l S ' C ' - e |tC si+ 2 Zc, ? z - J2- (UitO C^ ) d x and S' e/*

Math 106 Midterm Exam #3 2017

Related Documents

Description

Related Documents

Free up your schedule!

Take 5 seconds to unlock