31B midterm1-sols

# 31B midterm1-sols - MATH 31B LECTURE 4 MIDTERM 1 Name...

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Unformatted text preview: MATH 31B, LECTURE 4 MIDTERM 1 JANUARY 30, 2012 Name: Solutions UID: TA: (circle one) Huiyi Hu Brent Nelson Andrew Ruf Discussion meets: (circle one) Tuesday Thursday Instructions: The exam is closed-book, closed-notes. Calculators are not permitted. Answer each question in the space provided. If the question is in several parts, carefully label the answer to each part. Do all of your work on the examination paper; scratch paper is not permitted. If you continue a problem on the back of the page, please write “continued on back”. Each problem is worth 20 points. Problem Score 1 2 3 4 5 Total 1 2 Problem 1: (a) Let f ( x ) = √ x 3- 2 x + 5 for x ≥ 0. If g ( x ) is the inverse of f ( x ), find g (2). (b) Find the derivative of sec- 1 x at x = 2. Solution : (a) To find g (2), set f ( x ) = 2: p x 3- 2 x + 5 = 2 ⇒ x 3- 2 x + 5 = 4 ⇒ x 3- 2 x + 1 = 0 ⇒ x = 1 . We have f ( x ) = 3 x 2- 2 2 √ x 3- 2 x +5 so f (1) = 3- 2 2 √ 4 = 1 4 . We then have g (2) = 1 f (1) = 1 1 / 4 = 4...
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31B midterm1-sols - MATH 31B LECTURE 4 MIDTERM 1 Name...

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