c Kathryn Bollinger November 10 2010 Week In Review 8 4 6 4 8 5 1 5 2 1 Find two non negative numbers x and y whose sum is 50 and f xy 2 2y 3 is a Minimized if possible b Maximized if possible 1 c Kathryn Bollinger November 10 2010 2 2 A new soft drink company wants to make a new drink and sell it in a non standard size cylindrical can The can must hold 24 cubic inches of soda It costs the company 0 50 in2 to make the top of the can 0 25 in2 to make the bottom of the can and 1 in2 for the side of the can Use calculus to determine the size of the can which should be used in order to minimize the company s costs c Kathryn Bollinger November 10 2010 3 Find the most general antiderivative for the following functions 1 5 a f x csc2 x x4 e2 7ex x b g x 3 x2 x 2 x sec2 x x3 c h x x 2x2 6x 8 9 sec x tan x 3x 3 4 c Kathryn Bollinger November 10 2010 4 Find f x if f x 2 x2 and f 1 2 x4 5 Find f x if f x 2ex sin x f 0 7 f 0 5 cos 0 1 and sin 0 0 c Kathryn Bollinger November 10 2010 5 6 If a ball is thrown upward with an initial velocity of 30 ft sec from 15 feet above the ground find the speed of the ball when it hits the ground 6 c Kathryn Bollinger November 10 2010 7 Approximate the area under the curve y x2 2x and above the x axis from x 2 to x 4 by a Riemann sum with 4 equally spaced subintervals using a Left endpoints as the sample points b Right endpoints as the sample points c The Midpoint Rule d What definite integral is being approximated by these sums What does it represent e What would Z 0 4 f x dx represent for this function 7 c Kathryn Bollinger November 10 2010 8 Express Z 2 10 h i cos 3x x2 dx as a limit of sums 9 The velocity of a car accelerating from rest to a speed of 60 mi hr over a period of 30 seconds is given below Time s Velocity mi hr 0 0 5 15 10 30 15 45 20 60 25 60 30 60 a Give an estimate for the distance traveled during the 30 seconds by using the velocity at the beginning of each 5 second time interval Is this approximation an upper or lower estimate of the distance traveled b Find the exact distance traveled during the 30 seconds 8 c Kathryn Bollinger November 10 2010 10 Using the given graph of f x calculate the following a b Z Area A 1 37 Area B 2 45 Area C 0 84 Area D 1 44 Area E 3 2 f x dx a A E C a b Z 0 Z 0 Z e Z c 2f x dx b c f x dx a d f x dx 0 e f x dx d f The area between f x and the x axis from a to e b B c D d e 9 c Kathryn Bollinger November 10 2010 11 Z 4 Z x dx 8 0 0 a 4 Z 4 Z 0 Z 4 3x2 dx 0 b 4x2 dx 6 c 0 x2 7x dx 12 Evaluate Z 3 4 x dx x2 dx 64 3 and Z 4 6 x2 dx 152 3 calculate the following 10 c Kathryn Bollinger November 10 2010 13 Find bounds to estimate the value of Z 6h 3 i x 4 2 9 dx
View Full Document
Unlocking...