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Unformatted text preview: Homework # 3 Due: 6/6/06 1. Find an equation of the tangent line to y = √ 2 x + 1 at the point (4,3). The equation of a tangent line to y = f ( x ) at ( a, b ) is ( y b ) = f ( a )( x a ). First, we write the equation as y = (2 x + 1) 1 2 d dx (2 x + 1) 1 2 = 1 2 (2 x + 1) 1 2 (2 x ) = (2 x + 1) 1 2 Evaluated at x = 4, we get (2(4) + 1) 1 2 = 9 1 2 = 1 3 . So the tangent line is y 3 = 1 3 ( x 4) 2. Draw a graph of a function f that has the properties g (0) = 0 g (0) = 3 g (1) = 0 g (2) = 1 3. Use the limit definition of the derivative to compute f ( a ) if f ( x ) = x 2 +1 x 2 f ( a ) = lim h → f ( x + h ) f ( x ) h = lim h → ( x + h ) 2 +1 x + h 2 x 2 +1 x 2 h = lim h → ( x + h ) 2 +1 x + h 2 ( x 2 x 2 ) x 2 +1 x 2 ( x + h 2 x + h 2 ) h = lim h → (( x + h ) 2 + 1)( x 2) ( x 2 + 1)( x + h 2) h ( x + h 2)( x 2) = lim h → ( x 2 + 2 xh + h 2 + 1)( x 2) ( x 2 + 1)( x + h 2) h ( x + h 2)( x 2) = lim h → x 3 + 2 hx 2 + x 2 h 2 + x 2 x 2 h ( x = lim...
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 Spring '08
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 Calculus

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