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Exam_exam_3_-1

Exam_exam_3_-1 - MATH 140 Dr Ellis INSTRUCTIONS THIRD EXAM...

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Unformatted text preview: MATH 140 Dr. Ellis INSTRUCTIONS: THIRD EXAM APRIL 21, 2003 1. Write your name and TA’s name on every answer sheet. 2. Answer each problem on a separate answer sheet. 3. SHOW WORK AND GIVE REASQJNS. NO CALCULATORS. [17] 1. (a) (b) [17] 2. (a) [so] 3. (a) Find the function f such that f ’(x) = 2sinx+ seczx and f(0) = 3. Find the horizontal atsymptote(s) of the graph of = 2x2+5 y 3—x2. Suppose a population is growing exponentially with P(O) = 1,000,000 and P(2) = 2,000,000. Find P(3). Let f be continuous; on [0, 2] and differentiable on (0,2). What does the Mean Value Theorem state about f? Let ﬂx) = 2x3 — 3x2 + 6. Find the maximum and minimum values of f on [—1, ]. Find the area of the largest rectangle that has two sides on the positive x axis and the positive y axis one vertex at the origin and one vertex on the curve y = e“". Explain carefully how you know the value you found in (b) is the maximum area. ‘ CONTINUED ON THE BACK [36] 4. Let ﬁx) = x4 + 2x3 + 1 (a) Find the intervals on which f is increasing and the intervals on which f is decreasing. (b) Find the points (if any) at which f has relative extreme values. (0) Find the intervals onl which f is concave upward and the intervals on which f is concave downward. (d) Find the inflection points (if any) of the graph of f. (9) Sketch the graph of f, being sure to use the information from (a) - (d). Notice thati ﬂO) = 1 and ﬂ—3/2) = —-11/16. mrh:4/O3 a:140x3ellisSpO3 ...
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Exam_exam_3_-1 - MATH 140 Dr Ellis INSTRUCTIONS THIRD EXAM...

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