7 Questions of Calculus 1 - Exam 1 | MATH 141, Exams of Mathematics

Download 7 Questions of Calculus 1 - Exam 1 | MATH 141 and more Exams Mathematics in PDF only on Docsity! Recitation Time PRINT your name Math 141, Exami, Spring 2009 The exam is worth a total of 50 points. There are 7 questions on 3 pages. SHOW your work. Make your work be coherent and clear. Write in complete sentences whenever this is possible. [CIRCLE| your answer. CHECK your answer whenever possible. No Calculators. I will post the solutions on my website a few hours after the exam is finished. 1. (7 points) Parameterize the curve pictured below. Use ¢ as your parameter with 0 <t<2. The point that corresponds to t= 0 is (0,0). The point that corresponds to t = 1 is (1,1). The point that corresponds to t = 2 is (0,1). (Note: Each part of the curve that looks like a line segment is a line segment.) (0,1) Ct) (0,2) 2. (7 points) Express sin(@+) in terms of sin@, siny, cos@, and cosy. 2 3. (7 points) Compute lim, =. 36—a 4. (7 points) Compute lim we 26> 5. (7 points) Let f(z) = 22?+3. Find fel Oe and simplify as much as possible.