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V63_0121_0034_2008F_Midterm

# V63_0121_0034_2008F_Midterm - x> 2 Where is this function...

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Calculus I Midterm Exam Exercise 1 Compute the following limits; they might be finite, infinite, or not exist. 1) lim x 0 x 2 - 4 x x 2 - 3 x - 4 2) lim x + x 2 - 1 x 3 + 3 x + 4 2) lim x 3 x + 1 - 2 x - 3 4) lim x 0 1 x - 1 x 2 + x 1

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Exercise 2 What are the (horizontal or vertical) asymptotes of the graph of the function f ( x ) = x + 1 ( x 2 - 1) 2 ? 2
Exercise 3 Compute the derivatives of 1) ( x + 1) 6 ( x + 2) 3 2) cos( x ) x 3) ( x 4 + 1) 1000 4) tan(cos( x ) + 1) 3

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Exercise 4 Find the tangent to the graph given by 2 x 2 + xy + y 2 = 4 at the point (1 , 1). 4
Exercise 5 1) Use transformations to sketch the graph of the function f ( x ) = braceleftbigg 1 2 x +2 if x

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Unformatted text preview: x > 2) Where is this function continuous? 3) Where is it diFerentiable? 5 Exercise 6 A triangle ABC is deforming as time goes by in the following way: • the angles in A and B are equal • the distance AB is Fxed to 1 • the distance AC is equal to the distance BC is equal to t for any time t ≥ 0. 1) Make a picture. 2) Using the intemediate values theorem, show that there is a time t at which the distance BC is half the distance AB . 6...
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