V63_0121_0001_2008F_Midterm_I

V63_0121_0001_2008F_Midterm_I - a of your choice? 3. (18%)...

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CALCULUS I Prof. E. Hameiri Mid-Term Exam I Fall, 2008 1. (20%) Let f ( x )=3 x 2 2 x +1. (a) Write an equation of the line going through the points (1 ,f (1)) and (2 ,f (2)). (b) Find a point on the graph of f where the tangent line to the graph has the same slope as the line in part (a). Write the equation of the tangent l ineatthatpo int . 2. (24%) (a) Graph the function f ( x )= | x 1 | . (b) Is f ( x ) continuous? Is it di±erentiable? Explain. (c) Let F ( x )= ( | x 1 | ,x 1 2 x + a, x > 1 . What value should be assigned to the number a to make f continuous? (d) Is
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Unformatted text preview: a of your choice? 3. (18%) Evaluate the following limits: (a) lim x →−∞ 5 x 2 − 7 x + 2 x 2 − 6 x + 2 , (b) lim x →− 3 x 2 − x − 12 x + 3 , (c) lim x → tan x x 2 + x 4. (24%) Find dy/dx for: (a) y = 3 x 5 − 3 x 2 √ x + 2 √ x + π 2 , (b) y = 2 sin x + cot x , (c) y = ( x 2 + 3 x + 1) sin x , (d) y = 3 x 2 − 2 x + 1 x 2 + 4 , 5. (14%) Compute the derivative of the function f ( x ) = √ x + 1 from the de²nition (using the limit h → 0)....
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This note was uploaded on 10/25/2010 for the course MATH V63.-0121- taught by Professor Staff during the Fall '08 term at NYU.

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