6 Questions Exam 1 - Calculus I | MATH 170, Exams of Calculus

Download 6 Questions Exam 1 - Calculus I | MATH 170 and more Exams Calculus in PDF only on Docsity! Name: Exam 1 - Math 170 Oct 1, 2008 R. Ketchersid Instructions. Show all work for any partial credit. Where appropriate indicate your final answer by putting a box around the answer. Do not leave two answers and expect me to pick the correct one for you. Feel free to use your calculator to check answers, but I want exact solutions to all problems. If anything is unclear ask me about it. 1. [10pts] Compute f ′(x) for f(x) = 3x2 + 1 using one of the two limit definitions of derivative given in class. 2. [5pts] If you zoom in at (1, 4) on the graph of y = 3x2 + 1, then the graph looks like a straight line. What is the equation of this line? 3. [5pts] What does it mean to say “f(x) is continuous at x = a”? - 2 - 4. [10pts] Consider the function f(x) = x2 − 9 x2 + x− 6 You don’t need to show work on each part, you will either get it correct or not. a) [2pts] Where is f(x) continuous? (Use interval notation.) b) [2pts] Where is f(x) > 0? Use a sign diagram for f(x). c) [2pts] Are there any vertical asymptotes? If so what are they? d) [2pts] Are there any horizontal asymptotes? If so what are they? e) [2pts] Sketch the vertical and horizontal asymptotes and roots of f(x). Using this information and your sign diagram sketch a rough guess at what the function looks like.