Homework 3 - x = 4 g ( x ) = b x 2-16 x +4 if x n = 4 , 8...

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INSTRUCTOR: JOS ´ E MANUEL G ´ OMEZ Homework 3. Due date Wednesday September 21, 2011 Please show all your work. (1) (10 Points) Determine if the following limits exist. When they do Fnd their value (a) lim x 2 e x +2 . (b) lim x 3 + x 3 27 x 3 . (c) lim x 0 e x + 1 3 x + 1 . (d) lim x 2 + 1 x 2 . (e) lim x 0 x + 1 1 x . (2) (5 Points) Consider the function f ( x ) deFned below f ( x ) = 1 x 2 if x > 1 , 0 if x = 1 , x 3 x if x < 1 . Determine if the following quantities exist. In case they exist, Fnd their values. (a) lim x 1 + f ( x ), (b) lim x 1 - f ( x ), (c) lim x 1 f ( x ) . (3) (5 Points) Determine if the function g ( x ) deFned below is continuous at
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Unformatted text preview: x = 4 g ( x ) = b x 2-16 x +4 if x n = 4 , 8 if x = 4 . (4) (10 Points) The function h ( x ) is deFned as follows h ( x ) = x +2 x +1 if x &gt; , 2 if x = 0 , e x + c if x &lt; . 1 2 INSTRUCTOR: JOS E MANUEL G OMEZ (a) Find the value of c such that lim x h ( x ) exists. Please explain your answer. (b) Suppose now that c is the number you found in part (a). Is the function h ( x ) continuous at x = 0. Please explain your answer....
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Homework 3 - x = 4 g ( x ) = b x 2-16 x +4 if x n = 4 , 8...

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