Midterm 1 Exam - Midterm I Laurence Field Math 152, Section...

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Midterm ILaurence FieldMath 152, Section 31January 27, 2012Name:Instructions:This midterm has 6 questions for a total of 60 points.The value of each part of eachquestion is stated. Please show your working.QuestionPointsScore1721331041251266Total:60i
1.(a) (7 points) Find the intervals on which the functionf(x) =x3-3xis increasing, decreasing, concave up and concave down respectively. Also find any points of inflec-tion of the graph off.2. Calculate the following integrals. You may use the Fundamental Theorem of Calculus.(a) (4 points)Z415x2-12xdx1
(b) (4 points)Z0-π/4sec2x dx(c) (5 points)Z20f(x)dxwheref(x) =(x,x1,1/x2,x >1.2
3.(a) (8 points) Letnbe a positive integer. Letf(x) = 1/xforx[1,2n]. Find the lower and uppersums offon the partitionP={1,2,4,8, . . . ,2n-1,2n}of [1,2n].(b) (2 points) Use part (a) and the definition of the integral to show thatn2Z2n11xdxn.You maynotuse the Fundamental Theorem of Calculus.3
4.(a) (5 points) Find the total area enclosed between the
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Term
Fall
Professor
townsend
Tags
Math, Calculus, Derivative, Mathematical analysis, Convex function

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