Solutions Test 2B - Solutions to Test 2 Version B Math 1501 Fall 02 WG Exercise 1(a Assume that f x = √ 5 x Then f(1 h f(1 h = √ 4 h √ 4 h We

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Unformatted text preview: Solutions to Test 2, Version B Math 1501, Fall 02. WG * October 17, 2002 Exercise 1. (a) Assume that f ( x ) = √ 5- x. Then f (1+ h )- f (1) h = √ 4- h- √ 4 h . We multiply and divide the right handside of the equality by the conjugate of √ 4- h + √ 4 to obtain that f (1 + h )- f (1) h = ( √ 4- h- √ 4)( √ 4- h + √ 4) h ( √ 4- h + √ 4) =- h h ( √ 4- h + √ 4) . Simplifying by h, we deduce that f (1) = lim h → f (1 + h )- f (1) h = lim h →- 1 √ 4- h + √ 4 =- 1 4 . (b) If f ( x ) = x + 1 if x ≤ - 1 ( x + 1) 2 if x >- 1 then f- (- 1) = ( x + 1) | x =- 1 = 1 , f + (- 1) = [( x + 1) 2 ] | x =- 1 = 2( x + 1) | x =- 1 = 0 . Since f- (- 1) 6 = f + (- 1) we deduce that f (- 1) does not exist. Exercise 2. Call Δ c the tangent line at c to the graph of x → f ( x ) = x 3- 3 x. Then the equation of Δ c is Δ c : y- f ( c ) = f ( c )( x- c ) , * School of Mathematics, Georgia Institute of technology....
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This note was uploaded on 02/07/2011 for the course MATH 1501 taught by Professor N/a during the Fall '08 term at Georgia Institute of Technology.

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Solutions Test 2B - Solutions to Test 2 Version B Math 1501 Fall 02 WG Exercise 1(a Assume that f x = √ 5 x Then f(1 h f(1 h = √ 4 h √ 4 h We

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