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Homework 5

# Homework 5 - x 2-6 x-2 where the tangent line is...

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MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2011 INSTRUCTOR: JOS ´ E MANUEL G ´ OMEZ Homework 5. Due date Wednesday October 12, 2011 Please show all your work. (1) (5 Points) Consider the function f ( x ) = | x | . (a) (3 Points) Compute lim h 0 - f ( h ) - f (0) h and lim h 0 + f ( h ) - f (0) h . (b) (2 Points) Use the above to conclude that f (0) does not exist even though f is continuous everywhere. (2) (10 Points) Compute the derivatives of the following functions. (a) (2 Points) a ( x ) = 2 x 2 cos( π 2 ) + ex 3 . (b) (2 Points) b ( t ) = t + 1 t . (c) (2 Points) c ( x ) = x + 1 x 2 - 2 . (d) (2 Points) d ( x ) = x ( x 2 + 1) . (e) (2 Points) e ( s ) = s 1 / 2 - s 1 / 2 s 2 + 1 . (3) (5 Points) Find the point or points in the parabola with equation y
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Unformatted text preview: x 2-6 x-2 where the tangent line is horizontal. (4) (10 Points) Consider the function g ( x ) de±ned by g ( x ) = 2 x 3 3 + 5 x 2 2 + x-2 . Find the point or points ( x , y ) in the graph of g ( x ) in such a way that the tangent line to the graph of g ( x ) at the point ( x , y ) is parallel to the line y = 4 x-2. (5) (10 Points) Let h ( x ) = x 2 + 1. Find the point or points ( x , y ) in the graph of h ( x ) in such a way that the tangent line to the graph of h ( x ) at the point ( x , y ) passes through the point (0 , 0). 1...
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