Exam 4 with Answer Key - Analytic Geometry and Calculus II | MATH 175, Exams of Analytical Geometry and Calculus

Download Exam 4 with Answer Key - Analytic Geometry and Calculus II | MATH 175 and more Exams Analytical Geometry and Calculus in PDF only on Docsity! Exam average Quiz average Grade __ Math 175-02 Name ] Exam #4; Fall 2000 12-7-00 Show your work. Put a box around your answer. 1.(10 %) Eliminate the parameter to find the Cartesian, ie., (x,y) equation of the following parametric curve. Sketch the curve. 2 = sint, y=cos’t, O<t<2n. wns t set =/ ag -lex<l BOG! } oe yet Xe \ Opi. = Lay - --- Xx Li Cyemb Of 2.(10 %) Find the equation of the tangent (slope) to the curve a = 3é? +1, y = 2¢3 + Lat the point (4, 3). xe = LG/ +4 or c3/ fal (¢ i/ por Beles or bef C1 oo / ee Of. ff. Ef f= Ae xX Et “ / / (4,3 ) 3.(15 %) Use the parametric equations of the cycloid, given byr= 6—sin8, y=1—cosé, 0 <4 < 2n to find the area that it encloses. HINT ; Remember: cos? = (1 + cos 26). Xl b= CE B aa a / f_ o Ae [lye rattle « [(-cest) (ete JAB - x ° oi oe - fo “Line + Cone \Ae C ~ ey ty COLL E del & x ¢ 3 ; / oe /” ER > PINE fa SE x 4 / - a“ 324 SY. By C x a 4.(20 %) (a) Use the Maclaurin series for cosz = z et 22” to find the number series for fo TI cos (x?) dz. (b) Approximate the value of the “integral by the first three terms of the series. Aart o ney ¥\, ae 4n fe 3 ee a1)" ane - (fy CAC FF texte a pa th “ a von hart Bh 57 (-i)" (= [ot ocds “Zeculn e, ue oe f 4 i ft (i 3 ‘ | = G25 () spe coh —_ Lae 5,(20 % ) (a) Find the Taylor polynomial of degree n ns = 2 of f(z) = vite about a = 0. (b) Use Taylor's remainder |R,.(x)| < may jc — a["+? where |f*)(x)| < M to Vite fordO<2<01. i estimate the accuracy of the approximation f(x) * [ Lf) { } —--4 1 | Oo | pod poof 2 i 1 i | aa | 2} “hy / [ x)= 3 nc ee ne 3 : a wet ca see FOr sae ~ & . 3 7. 43 / a 2 OS 57) = ge en [ecee cuca |