31B pmidterm1-sols

# 31B pmidterm1-sols - MATH 31B LECTURE 4 PRACTICE MIDTERM 1...

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Unformatted text preview: MATH 31B, LECTURE 4 PRACTICE MIDTERM 1 JANUARY 22, 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) Find the derivative of cos- 1 x at x = √ 2 2 . (b) If g ( x ) is the inverse of f ( x ) = x 3 + x + 1, find g (1). Solution: (a) cos- 1 ( √ 2 2 ) = π 4 . Since d dx cos x =- sin x , (cos- 1 ) √ 2 2 = 1- sin π 4 =- 2 √ 2 =- √ 2 . (b) To find g (1), set f ( x ) = 1: x 3 + x + 1 = 1 ⇒ x = 0 We have f ( x ) = 3 x 2 + 1, f (0) = 3 · 0 + 1 = 1 so g (1) = 1 f (0)...
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31B pmidterm1-sols - MATH 31B LECTURE 4 PRACTICE MIDTERM 1...

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