exam1_fa05

# exam1_fa05 - = √ 16 x 2 1 x 3(a Identify the vertical...

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Name: Section Number: TA Name: Section Time: Math 20A. Midterm Exam 1 October 19, 2005 You may use one page of notes, but no other assistance on this exam. Turn oF and put away your cell phone. Read each question carefully, answer each question completely, and show all of your work. Write your solutions clearly and legibly; no credit will be given for illegible solutions. If any question is not clear, ask for clari±cation. 1. (6 points) Consider the function f ( x ) = 7 - x . (a) Find the domain and range of f . (b) Find f - 1 , the inverse function of f . Be sure to clearly state the domain and range of f - 1 . # Score 1 2 3 4 5 6 Σ

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2. (4 points) Let g be a function such that g (1) = 3 and g 0 (1) = - 5. (a) Find an equation for the line tangent to the graph of g at the point (1 , 3). (b) Find the value of lim x 1 g ( x ) - g (1) x - 1 .
3. (8 points) Let f ( x

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Unformatted text preview: ) = √ 16 x 2 + 1 x + 3 . (a) Identify the vertical asymptotes of the graph of f by calculating the appropriate limits. (b) Identify the horizontal asymptotes of the graph of f by calculating the appropriate limits. 4. (6 points) Let a > and consider the function f ( x ) = ( 3-ax 2 if x < 1 , a x + 2 if x ≥ 1 . Find the value of a for which f is continuous and explain why the value of a that you found makes f continuous. 5. (6 points) Find the exact value of lim x → √ 5-x-√ 5 x . Justify your answer. 6. (6 points) Let f ( x ) = 1 2 + 5 x . Use the defnition oF the derivative to compute f ( x ). (Note: Computing the derivative without evaluating the appropriate limit will not earn any credit.)...
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exam1_fa05 - = √ 16 x 2 1 x 3(a Identify the vertical...

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