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Homework 3

# Homework 3 - x = − 4 g x = b x 2-16 x 4 if x n = − 4...

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MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2011 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 find 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 ) defined 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, find 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 ) defined 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 > , − 2 if x = 0 , e x + c if x < . 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...

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