Math 150B: Exam 1 Solution

Exam (1)Math 150B. Calculus IISection # 18056 Fall2022Instructor: Henrik SarkssianMoruoRy SeprE^aeER26, I 2:3O PM -1:35 PMName:- ShOW(Please print)all Of yOUf WOrk and make the final answers clear. Full credit will Nor be givenfor merely stating the right answer without any appropriate justification.- Cell phones must not be visible or audible at any time during the exam. This applies to all smarttechnology including watches, cameras, and pens.NoCa lculators!Problem123456TotalMaximum[2s]t2sI[2s][2s]t2sI[2s]150ScoreExam (1) Math 150B. Calculus II Section # 18056 Fall 2022 Instructor: Henrik Sarkssian MONDAY SEPTEMBER 26, 12:30 PM - 1:35 PM Name: Answer key (Please print) - Show all of your work and make the final answers clear. Full credit will NOT be given for merely stating the right answer without any appropriate justification. - Cell phones must not be visible or audible at any time during the exam. This applies to all smart technology including watches, cameras, and pens. No Calculators! Problem 1 2 3 4 5 6 Total Maximum [25] [25] [25] [25] [25] [25] 150 Score 1

Problem 1. (25 pts.)Evaluate the derivative of the function. (DO NOT SIMPLIFY!)f (x) = 3ln(x2 + 1) + cos-'1e*;,1r9nLx'tllr-("r),ooProblem 1. (25 pts.) Evaluate the derivative of the function. (DO NOT SIMPLIFY!) f(x) = + cos- (e*) 3 (2x) i - ex f(x) = + x2+1 (1-(e*) 12 12 2

Problem 2. (25 pts.)Evaluate the integral.I *r S.v \,Jsin-'xdxLn,s u{- Jv/" ,=xgn}n1v)rh^S+'^*x-f)6{ry Offi rct^sH,- xglnl tr + t + c=Av-drOx)ctrot-Gl'^- l-\Lz+"lt = -zdh_rd*- YAx6Problem 2. (25 pts.) Evaluate the integral. sin xdx us Sin't dr.dx 5 due nox 51-x2 = an- Svdu , = xSin'x x - S V1-X2 x dx tovi-xe 5 t?:- 1-x2 5 2tdt I -2xdx -tdt = xdx = + 5 x Sin'x+ 1-x2ch 5 3

Problem 3. (25 pts.)Find the limit using L'Hopital's rule. Show all of your work.l1B(,**)"n*h49,v'x- {"ilr{,r^Ll^n)6,e--Lu5gxaO'-?-v".=e*-Ory(5)t-?rt"dauV@a(5)zJ.9."t-_E_+coes@fr,(10')/u..,U*rr/)ee.'toc scF(s-t*loo0X-+6't5L/De-Fe-{l€,4Problem 3. (25 pts.) Find the limit using L'Hopital's rule. Show all of your work. lim (tan x)sinx x-0+ In (tanx) Sinxtu (tans) -00 lim csex +00 5 lim e 5 , e x+0+ e 5 5 5 x-10+ 5 L'Hop See'x - See'x lim tant Gim CSCX 00 x10+ -esex Cats X-10+ 0 = e in e 5 e se 5 5 5 4

Problem a. (25 pts.)Evaluate the integral.Jsinuxcos3 xdx&r,6*us 9nx?ur\ %v/txr'-.i\)/*6- Atro/x(.n', (l -w ?r)rluC12.T uG (t -u'1du z { "'a-l*e5Y',l-€f_rc,s&7+Q_8,- u/a@q4€'-t'?'PLProblem 4. (25 pts.) Evaluate the integral. sin x cos ³ xdx S smix los losxdx us Sixx 5 5 s 5 8 5/2 = Sub u a du i s/t 7 9 1/4 +C - Smk, Sm x 7 pe 5 9 5

Problem 5. (25 pts.)Evaluate the integral.JJr-*a,XtQrn\lo.A4a&96,Z-fi&g5I 6,fiUos Jz[:,wr ),?,[--".r )[,@o?--f lryad e t r ry+c sqrW*coZr--;orrLr^n+ I-/ ''" nt6,Problem 5. (25 pts.) Evaluate the integral. xs sno dxs Cosodo I 5 V1-x2 Coddo = S los odo 5 5 5 Sido t fla 5 No Sin20 4 +C smolosd zel 5 = 1 aresims + x/1-x c + 5 6

P roblem 6. (25 pts.)E valuate the integral.6xJ (x+l)(x2+2)dxa6r?.k-t l) (;.'tf