Question 9 use lhospitals rule to find the limit lim

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Question 9 Use l’Hospital’s rule to find the limit lim x 0 + x 2 ln x Answer: . . . . . . . . . . . . . . . . . . . . . Question 10 Use l’Hospital’s rule to find the limit lim x 0 + x x 2 Answer: . . . . . . . . . . . . . . . . . . . . . . . .

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CALCULUS I, TEST III 4 PART II Each problem is worth 10 points. Part II consists of 5 problems. You must show your work on this part of the test to get full credit. Displaying only the final answer (even if correct) without the relevant steps will not get full credit. Problem 1 Use logarithmic differentiation to find y if y = ( x + 1) 4 e x x 2 - 1
CALCULUS I, TEST III 5 Problem 2 Use logarithmic differentiation to find y if y = [cos x ] sin x

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CALCULUS I, TEST III 6 Problem 3 Simplify y = cos(arcsin x ), then find y . For an extra credit, find y in two ways: before simplification and after simplification. Do your answers agree?
CALCULUS I, TEST III 7 Problem 4 Use a linear approximation of the function f ( x ) = x at an appropriate point to approximate the value of 25 . 1

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CALCULUS I, TEST III 8 Problem 5 Use Newton’s method with the initial approximation x 1 = 0 to find x 2 , the second approxi- mation to the root of the equation x 3 + 3 x + 3 = 0 For an extra credit, find x 3 , the third approximation to the root.
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