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Unformatted text preview: Practice Final Exam for Math 1501, Calculus I PART ONE CORRESPONDING TO TEST ONE (I): Let f ( x ) = ( Ax- B if x 1, 3 x if 1 < x < 2, Bx 2- A if x 2 . (a) Determine all values of A and B that make this functions continuous. (b) Determine all values of A and B that make this functions continuous at x = 1 but discontinuous at x = 2. (II): Determine whether the following limits exist. When they do exist, evaluate the limit. (a) lim x ( x- x + 1) (b) lim x sin 3 ( 2 x ) x 3 (c) lim x 2 x ln( x )- 2 ln(2) x- 2 PART TWO CORRESPONDING TO TEST TWO (III): Consider the curve given by x 4 + y 4 = 1 . (Note the fourth powers; this is not the unit circle.) (a) Find the points where the line y = 2 1 / 4 x crosses this curve. (b) Find the equation for the tangent line to the curve at each of the points found in part (a). (IV): A ladder 5 meters long is leaning against a wall. If the foot of the ladder is pulled away from the wall at a rate of 1 meter per second, how fast will the top of the ladder be...
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- Fall '08