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exam1_fa07

# exam1_fa07 - Name TA Math 20A Midterm Exam 1 November 1...

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Name: PID: TA: Sec. No: Sec. Time: Math 20A. Midterm Exam 1 November 1, 2007 Turn o ff and put away your cell phone. No calculators or any other electronic devices are allowed during this exam. You may use one page of notes, but no books or other assistance during this exam. Read each question carefully, and answer each question completely. Show all of your work; no credit will be given for unsupported answers. Write your solutions clearly and legibly; no credit will be given for illegible solutions. If any question is not clear, ask for clarification. 1. (6 points) Let f ( x ) = e 2 x and g ( x ) = 2 ln( x ). (a) Find the domain and range of f ( x ). (b) Does f ( x ) have an inverse function? Justify your answer. (c) Are the functions f ( x ) and g ( x ) inverses of each other? Explain how you determined your answer. # Points Score 1 6 2 6 3 6 4 8 5 6 Σ 32

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2. (6 points) For each of the following limits, either evaluate it or explain why it does not exist. (a) lim x 0 1 2 x - 1 x ( x + 2) (b) lim x 7 2 x 2 x - 7 (c) lim θ 0 θ sin( θ ) 1 - cos(2 θ )
3. (6 points) Suppose that f ( x ) is a function such that f (3) = 1 and f (3+ h ) - f (3) = h 2 + h e h . (a) Find f (3).

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exam1_fa07 - Name TA Math 20A Midterm Exam 1 November 1...

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