10 Questions Exam #2 - Calculus I | MATH 1441, Exams of Calculus

Download 10 Questions Exam #2 - Calculus I | MATH 1441 and more Exams Calculus in PDF only on Docsity! TS +0 Exam 2, Kersey, Math 1441, Fall 2007 Instructions: Show al] your work. Answers without appropriate supporting ‘work will récelvé partiar or no credit. You don’t need to simplify answers. 10. . Differentiate: (2) = 20074 + 27 — ¥z. . Differentiate: f(x) = sin(2x) Va? +1 . Differentiate: y = sec(sin(x”)) | Differentiate and simplify: y = 82) simp’) Y= Ty sin(z) . Find the derivative of f(z) = 1+ 2 using the formal definition. | Find the equation of the tangent line to 2? + y? = 2°y? +1 at (1.9-{0,¢) A stone is tossed into the air according to the equation s(t) = —16¢? + 64¢ feet at time t seconds. (a) Find the maximum height it reaches. (b) Find the velocity when it hits the ground. . Let e(t) = (2 cos(2¢), —3 sin(2t)). (a) Convert the curve to x-y coordinates and sketch plot. {b) Find the equation of the tangent line at ¢ = 7/6, and plot on your graph. . A 5 foot ladder is against a wall. The base is 4 feet from the wall and sliding away at 2 ft/sec. (a) How fast is the top sliding down? (b) Extra Credit: At what rate is the angle @ between the ladder and the ground changing? Find the linear approximation of f(z) = /z+1 at a = 3, and use this to estimate /4.1.