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Unformatted text preview: A Last Name:_______________________ Math 2A Final Exam Sample
First Name:____________________________________ Last Name:____________________________________ Student ID #:__________________________________ Section:______________________________________ I certify that this exam was taken by the person named and done without any form of assistance including books, notes, calculators and other people. __________________________________________ Your signature (For instructor use only!) Problem 1 2 3 4 5 6 7 8 9 10 TOTAL Score ID #:____________________________ This exam consists of 10 questions worth 10 points each. Read the directions for each problem carefully and answer all parts of each problem. Please show all work needed to arrive at your solutions. Label graphs and define any notation used. Clearly indicate your final answer to each problem. 1.) Determine the value of each of the following limits. 2.) Compute the indicated derivative of each of the following functions. (You do not need to simplify the result algebraically.) a.) , Find b.) , Find c.) , Find d.) , Find e.) , Find ID #:____________________________ 3.) Compute the indicated derivative of each of the following functions. a.) , Find (Simplify result to a single fraction.) b.) , Find 4.) a.) Given that the tangent line to find and . at passes through the point , b.) Sketch a graph of a continuous, differentiable function which satisfies: ID #:____________________________ 5.) Use implicit differentiation to find the equation of the tangent line to the curve at the point . 6.) For the function a.) Is the function continuity. , answer each of the following: continuous at ? Justify your answer using the definition of b.) Find all of the points of discontinuity of . c.) Use the Intermediate Value Theorem to verify that has a zero on the interval . d.) Find the equations for any horizontal and vertical asymptotes of this function. ID #:____________________________ 7.) Suppose that and for . Apply the Mean Value Theorem on the interval to prove that Also, prove more generally that for all . . 8.) A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius of the outer ripple is increasing at a constant rate of ft/sec. When the total area of the disturbed water is square feet, at what rate is the total area of the disturbed water changing? ID #:____________________________ 9.) According to postal regulations, a carton is classified as “oversized” if the sum of its height and girth (the perimeter of its base) exceeds 108 inches. Find the dimensions of a carton with a square base that is not oversized and has maximum volume. 10.) For the function a.) Find all intervals on which , answer each of the following: is increasing and intervals on which is decreasing. b.) Find any local maximum and minimum values. c.) Find all intervals on which is concave up and intervals on which is concave down. d.) Find any points of inflection. e.) Graph the function . ...
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