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MA_125_Test2

# MA_125_Test2 - x is horizontal(2 If a particle moves along...

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Name: Calculus I; Fall 2007 Part I Part I consists of 6 questions, each worth 5 points. Clearly show your work for each of the problems listed. (1) Find the equation of the tangent line to the graph of y = 3 x 2 + 2 x + 5 at x = 1. (2) If y = x sin( x ), ﬁnd y 0 . (3) If y = 3 x 4 + x 2 + 1, ﬁnd y 0 . 1

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(4) If y = x 2 +1 x 2 - 1 , ﬁnd y 0 . Simplify your answer. (5) If y = x 7 - 3 x 3 + x x , ﬁnd y 0 . Simplify your answer. (6) If y = sin(tan( x 3 + 1)), ﬁnd y 0 . [You don’t need to simplify the answer.]
Part II Part II consists of 5 problems each worth 14 points. You must show the relevant steps (as we did in class) and justify your answer to earn credit (1) Find all the x -values at which the the tangent line to the graph of y = 2 x 3 - 3 x 2 - 36

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Unformatted text preview: x is horizontal. (2) If a particle moves along the graph of y = sin(2 x ) + sec( x ) so that its x-coordinate is decreasing at a rate of 3 m/s , how fast is its y-coordinate changing when x = π/ 3? (3) If a ﬂash light is located on the ground 10 m from a building and shines a light on a man who is 2m tall and walks towards the building at a speed of . 2 m/s , how fast is the length of his shadow on the wall of the building changing when he is 3m from the building? (4) Find y if x 2 + y 2 = cos( xy ). (5) Find y if y = √ x 2 +1 x 2-1 . Simplify your answer....
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MA_125_Test2 - x is horizontal(2 If a particle moves along...

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