Exam 1 with Answers | Calculus and Analytic Geometry II | MATH 2423, Exams of Analytical Geometry and Calculus

Download Exam 1 with Answers | Calculus and Analytic Geometry II | MATH 2423 and more Exams Analytical Geometry and Calculus in PDF only on Docsity! Page 1 1(a) If r’(¢) is the rate of change of the radius of a spherical balloon measured in centimeters per 2 second, what does the integral [ r'(€) dé represent, and what are its units? 1 it represents the increase 10 rally 6 Behotecy for heist Select avol fox Secof scan , L DANts are Conrbureters a cos = (b) Find the derivatives of g(x) = f (1-2?) du and h(a) = | (Q-v?)" du. 1 1 gay = (1 -x~)'® eS hix) = aces x) ) hla) = gj (ces 4) F%.coF x = (sit )’Esikx ) = - 3)''x (c) Write down two different antiderivatives of f(x) = cos(,/x — 1). 2% t coSC Sent dee Oo a - % 5 cos( SET Jal | a Page 2 2(a) Find the area of the shaded region: ao , * Aten = (a-y)-6) dy a . = Sa-yt ty ds = zy ~3y oy o tray + 409” = 22) -a(27 + 32) _ _ 2 = lo ~ 4 4 + 2 13 (b) Sketch carefully the region or regions whose area is given by [ “ cos —sinz|dz. Then find this aféa. } A Atta = 5 (cose Slax oye ° rr + S [Sinx - Ca) abye 7 y TT Sin x +eosx } CE -SaK | o x JM 2 SinCEY) Ee coslBS -stte) -ces[0) — - ces (or) - Sin lor . ‘ a 4 cos (| + Sen es) z QUZ,