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Unformatted text preview: a ) lim x →1 1 + x 3 1 + x + x 2 + x 3 b ) lim x → π/ 2 sin(2 x ) xπ/ 2 c ) lim x → 2 x + 1 x 2 d ) lim x → √ 1 + x1 p 1 + ( x1) 22 e ) lim x → π/ 2 cos( x ) xπ/ 2 III: (25 points) Given the function f ( x ) = 1 √ 1x 2 . a) Find all values for x that satisfy  f ( x )1  < 1 b) Find g ( h ) so that  f ( h )f (0)  = g ( h )  h  c) For ε > 0, ±nd δ > 0 so that  h  < δ ⇒  f ( h )f (0)  < ε IV: (25 points) Prove, using Mathematical Induction, that1 + 2 23 2 + 4 2.. + (1) k k 2 + ... + (1) n n 2 = (1) n n ( n + 1) 2 . Fill in the following steps: a) Check the result for n = 1. b) Write the Induction Assumption: c) Carry out the induction step:...
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 Fall '08
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 Calculus, lim, Linear function, 50 Minutes

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