31B(F07)_PracticeMidterm1_Solutions

# 31B(F07)_PracticeMidterm1_Solutions - MATH 31B Lecture 4...

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MATH 31B - Lecture 4 - Fall 2007 Solutions to Practice Midterm 1 - October 22, 2007 This is a closed-book and closed-note examination. Calculators are not allowed. Please show all your work. Use only the paper provided. You may write on the back if you need more space, but clearly indicate this on the front. 1

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2 1. Let f ( x ) = 3 + x 2 + tan( πx 2 ) , - 1 < x < 1. Find the value of the derivative ( f - 1 ) 0 (3). Solution. Note that f (0) = 3 and f 0 ( x ) = 2 x + π 2 sec 2 πx 2 . Thus ( f - 1 ) 0 (3) = 1 f 0 (0) = 1 π/ 2 = 2 . / 2. You have just placed A 0 dollars in a bank account that pays 4% interest compounded continuously. (a) How much money will you have in the account in 5 years? (b) How long will it take for your money to triple? Solution. (a) In 5 years you will have A 0 e 0 . 2 dollars in the account. (b) Solving for t e 0 . 04 t = 3 we obtain t = 25ln3 years. /
3 3. Find the derivative of the function f ( x ) = (ln x ) x . Solution.

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31B(F07)_PracticeMidterm1_Solutions - MATH 31B Lecture 4...

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