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Continuous Function - Calculus I - Exam

Exams, Calculus I

Post: March 15th, 2013
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Continuous Function, Differentiable Function, Intermediate Value Theorem, Find Following Limits, Equation for Tangent Line, Position of Vehicle, Acceleration of Vehicle, Concave Downwards are some points from this exam paper of Calculus I.
Continuous Function, Differentiable Function, Intermediate Value Theorem, Find Following Limits, Equation for Tangent Line, Position of Vehicle, Acceleration of Vehicle, Concave Downwards are some points from this exam paper of Calculus I.
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MA 125-5B, Spring 2004 TEST # 1 February 6, 2004 (70 minutes) Name: SSN: Max. Points: 100 + 5 Bonus Points: Test Grade: Turn in all the work which you did to solve the problems, not just the final answer. In particular, include intermediate steps in calculations wherever they are needed. You may write on the back of a page if you need extra space. To receive credit, all solutions have to be based on the methods from Chapter 2 of Stewart’s book. No book, no notes, and no calculator are to be used! 1. (a) Define what it means that a function f is continuous at a number a. (3P) (b) Define what it means that a function f is differentiable at a number a. (3P) 2. State the intermediate value theorem. (6P) 3. Find the following limits: (4P+4P+4P+4P) x+2 (a) lim 2 x→−2 x − 4 (b) lim 1 x→0 cos x (c) xlim →∞ 2x3 − x 1 − 3x3 (d) lim 1 x→0 x3 4. From the graph of f provided on the right find all numbers a such that (3P+3P+3P+3P) (a) lim+ f (x) does not e..

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