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# CALCULUS I MA 113

UK

GPA 3.54

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This 7 page Class Notes was uploaded by Kennith Herman on Friday October 23, 2015. The Class Notes belongs to MA 113 at University of Kentucky taught by Staff in Fall. Since its upload, it has received 28 views. For similar materials see /class/228157/ma-113-university-of-kentucky in Mathematics (M) at University of Kentucky.

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Date Created: 10/23/15

MA1130257027 Russell Brown Review 1 September 167 1998 1 Let xm 4 and gm 032 1 Give the domain of Find fog and go 2 Sketch the graph of 103 Based on this graph7 nd graphs of 17 2f03 and f B 1 1 3 Suppose that a wheel of radius 1 meter rolls along the m aXis without slipping If the bottom of the wheel is initially at the origin7 nd the coordinates of the point P after the wheel has rotated through an angle of 7r4 Hint How far has the wheel travelled after it has rotated through an angle of 23141 4 Consider the parametric curve 13sint7 ycost a Make a graph of the curve and give an arrow to indicate the direction we move as t increases b Given an equation in as and y that every point on the curve satis es c Find a value oft where the y coordinate is as large as possible 5 A population doubles every 10 days and after 20 days7 the population is 400 a What is the population initially 13 c When does the population reach 20000 Give the size of the population after 23 days Solve 212 7 b Find 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dowel e asn mu XeLu 110 39Luexa aq ugmp Ie1wleo e asn XeLu 110 alaquwgdag zz Xepsani uo HI Hg u Lud 0g5 0 0g LUOJ s Luexa Inoq 4sq aqL 8551 U IaqLuaMog I MJAJH mm IPSWH 900 11003231 VIN 9 L39sc nduction t0 provc that 5quot 1 is a multipk of 1 for n 12 10 lfsc induction to provc that 22l 1c 277392 277 for n 12 11 11quot f is odd is f o f odd 1s 2f odd s f2 odd 12 Which of 1110 fbllowing functions arc Vt nl J r39 2 7t2quot cos 3quot sin 2quot MA1130257027 Russell Brown Review 4 September 167 1998 The final will be cumulative with an emphasis on Chapter 4 Below are review problems for Chapter 4 You will also want to study the review problems for the first three exams 1 Consider the function 034 032 Find all critical numbers Determine if each critical number is a local maximum7 local minimum or neither Find local maximum values and local minimum values Find intervals of increase or decrease Find intervals of concavity Find in ection points Sketch a graph using this information Check using TI 82 N Suppose a light is revolving at two revolutionsmin The light is three meters from a wall a Find the speed with which the light is moving along the wall when the beam forms a right angle with wall b Find the speed with which the light is moving along the wall if the light forms an angle of 45 with the wall 90 A rectangle is inscribed in the ellipse 2032 y2 1 Find the largest possible area of the rectangle 4 Find the global maximum and minimum values of sinm L on 0 7r 5 Suppose that a prism whose base is an equilateral triangle has volume 100 cm3 Find the small possible surface area 6 1 900 If we apply Newton s method to the following function starting a D7 which root will Newton s method find Same question for E and F Explain Newton s method and derive the formula mm as fwnf fvn Show how use Newton s method to find 3 10 Give 031 032 and 033 if 030 4 State the first derivative test for a global minimum Use this test to show that as 1an has a global minimum on 000 State the mean value theorem State the de nition of increasing function Use the mean value theorem to prove that if gt 0 for as E 0 17 then f is increasing on 07 1 Let 033 as for as in 22 Find the global maximum and minimum What are the global maximum and minimum values

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