10 Questions to Exam 2 - Calculus I | MATH 229, Exams of Calculus

Download 10 Questions to Exam 2 - Calculus I | MATH 229 and more Exams Calculus in PDF only on Docsity! MATH 229, Section 6 TEST II NAME Prof. J. Beachy 10/27/2000 NO CALCULATORS! Show all necessary work. 1. (20 points) Find the derivative f ′(x) or dy dx . (a) (p157 #14) f(x) = √ x− 1√ x (b) (p183 #17) f(x) = (3x− 2)10(5x2 − x+ 1)12. (c) (p215 #31) y = sin(tan( √ 1 + x3)) (d) (p187 Ex 2) x3 + y3 = 6xy 2. (5 points; p197 #17) Find the second derivative f ′′(x) for f(x) = tan(3x). MATH 229 Section 6 TEST I page 2 of 4 3. (6 points; p176 #40) lim x→0 tanx 4x = 4. (7 points; p157 #64) Find the equations of the tangent lines to the curve y = x− 1 x+ 1 that are parallel to the line x− 2y = 2. 5. (6 points; p211 #24) For y = √ 1− x, find the differential dy and evaluate dy for x = 0 and dx = 0.02. 6. (6 points; p217 #79) A window has the shape of a square surmounted by a semicircle. The base of the window is measured as having width 60cm, with a possible error of 0.1cm. Use differentials to estimate the maximum error possible in computing the area of the window.