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Unformatted text preview: Students Name: Final Exam (Wed, Dec 12, 5:30 pm - 7:30 pm, 106 LOVE) MAC2311, Section 17, Instructor: Ms. Hoa Nguyen (firstname.lastname@example.org) Problem 1 ( 7pts ) Find the limit, if it exists. Otherwise, write DNE. lim x - 1 x 2- 1 | x +1 | Problem 2 ( 5pts ) Find c such that f is continuous on (- , ). f ( x ) = cx 2 + 3 x if x &lt; 3 x 3- cx if x 3 Problem 3 ( 9pts ) Find the equations of the tangent lines to the curve x 2 + y 2 = 1 that pass through the point (0 , 2). Problem 4 ( 7pts ) Evaluate the limit: lim x ( xe 5 x- x ). Problem 5 ( 6pts ) Use logarithmic differentiation to find the derivative of the function y = x x . Problem 6 ( 10pts ) The area A of the region S that lies under the graph of the continuous function f ( x ) from a to b is the limit of the sum of the areas of approximating rectangles: A = lim n n X i =1 f ( x i ) 4 x a) Use this definition to find an expression for the area under the curve y = x 2 from 0 to 1 as a limit....
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- Fall '08