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# Calculus and Analytic Geometry I MATH 1823

OU

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This 13 page Class Notes was uploaded by Mason Larson DDS on Monday October 26, 2015. The Class Notes belongs to MATH 1823 at University of Oklahoma taught by Staff in Fall. Since its upload, it has received 29 views. For similar materials see /class/229297/math-1823-university-of-oklahoma in Mathematics (M) at University of Oklahoma.

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Date Created: 10/26/15

Sp3904 MATH 1823 020 Calculus I Dr Noel Brady Friday 02132004 Midterm 830am 920am student ID Instructions H No calculators or notes E0 Attempt all questions 00 Do not write on back of exam sheets Extra paper is available 7 Show all the steps of your work Clearly The method reasoning used to obtain an answer is worth more than the answer itself Question Points Your Score Q1 9 Q2 10 Q3 8 Q4 10 Q5 10 Q6 8 TOTAL 55 Q1 9 points Evaluate the following lirnit7 showing all your work 7 2 7 hm 2 l 2 zaZ 7 2 This limit represents the slope of the tangent line to the graph of some function at some point Determine a suitable function What is the point on the graph Draw a sketch of the graph Include the point and the tangent line Q2 10 points Compute the following limits Include the details of your work i x3h lim haO h 1 limw 2 ma272 Q3 8 points Give the precise de nition of the following limit the version involving a notion of closeness for output values7 6 and a notion of closeness for input values7 6 lirn f L mam Hint It starts like this We say that lirnmna x L iffor every 6 gt 0 there exists Use the precise de nition of a limit to show that lirg31 7 Q4 10 points The following graph represents the distance measured in miles that a car has traveled in time t measured in hours Answer the following questions7 giving reasons for your answers 1 At which if the three times A7 B7 D is the car traveling the fastest 2 At which if the three times A7 B7 D is the car traveling the slowest 3 What is the speed of the car at time B 4 At which of the 3 times 0 EF is the car accelerating 5 At which of the 3 times 0 EF is the car decelerating Q5 10 points Is the function continuous at z 0 Justify your answer Is the function continuous at z 0 Justify your answer Q6 8 points Compute the following limit Show details of your work hm E zal 3 7 1 Sp3904 MATH 1823 020 Calculus I Dr Noel Brady Friday 03122004 Midterm 830am 920am student ID Instructions H No calculators or notes E0 Attempt all questions 00 Do not write on back of exam sheets Extra paper is available 7 Show all the steps of your work Clearly The method reasoning used to obtain an answer is worth more than the answer itself Question Points Your Score Q1 12 Q2 10 Q3 12 Q4 10 Q5 11 TOTAL 55 Q1 12 points Compute the derivative f of each of the following functions Show details of your work we sine fx 3x 7 250z 340 5x32x3 z21 Q2 10 points Write down the limit de nition of the derivative the h a 0 limit form Write down the product rule formula is suf cient Give a proof of the product rule Q3 12 points Use implicit differentiation to nd y for the ellipse 22y2 2 Use implicit differentiation to nd y for the hyperbola 2x2 7 2y2 1 Show that the ellipse and the hyperbola above intersect orthogonally meet at right angles Q4 10 points Find the equation of the normal line to the graph of y 2 at the point 11 Key fact Normal line is perpendicular to tangent line at point of contact Verify that 30 lies on this normal line Which point on the parabola y 2 is closest to the point 3 0 Justify your answer say why your point is closer than all other points on the parabola Q5 11 points Evaluate the following limit by rst recognizing it as a derivative of some function tang h 7 1 lirn haO h Find an expression for the n th derivative f of the function

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