Calculus I Midterm Exam, MATH 1823-002, Noel Brady, September 24, 2010 - Prof. Noel Brady, Exams of Analytical Geometry and Calculus

Download Calculus I Midterm Exam, MATH 1823-002, Noel Brady, September 24, 2010 - Prof. Noel Brady and more Exams Analytical Geometry and Calculus in PDF only on Docsity! Fa’10: MATH 1823–002 Calculus I Noel Brady Friday 09/24/2010 Midterm I 10:30am–11:20am Name: Student ID: Instructions. 1. Attempt all questions. 2. Do not write on back of exam sheets. Extra paper is available if you need it. 3. Show all the steps of your work clearly. Question Points Your Score Q1 15 Q2 20 Q3 20 Q4 20 Q5 15 Q6 10 TOTAL 100 Q1]. . . [15 points] Let f(x) be a function of x whose domain is all real numbers. Consider the following expression. f(x) − f(2) x − 2 What is this expression called? Write down two interpretations of this expression. Q4]. . . [20 points] Compute the following limit. Show all the steps of your work. lim h→0 (2 + h)3 − 8 h Q5]. . . [15 points] Find the value of c which makes the following function continuous. Show the details of your reasoning. Keep in mind that the steps of your argument (how you arrived at a value for c) are more important than the actual value of c. f(x) = { 2x + 4 for x ≤ 1 cx2 + c for x > 1 Q6]. . . [10 points] Suppose that sin(θ) = 3/5 and that π/2 < θ < π. Find the values of cos(θ) and of tan(θ). Show the details of your work.