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# Calculus III MATH 2350

TTU

GPA 3.62

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This 3 page Class Notes was uploaded by Ms. Ally Koelpin on Thursday October 22, 2015. The Class Notes belongs to MATH 2350 at Texas Tech University taught by Lance Douglas Drager in Fall. Since its upload, it has received 12 views. For similar materials see /class/226462/math-2350-texas-tech-university in Mathematics (M) at Texas Tech University.

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Date Created: 10/22/15

40 pts 40 pts 40 pts Problem 1 Suppose that we want to hit a target 7000 feet away with a cannon that has a muzzle speed of 500 feet per second Find the two angles at which we can re the cannon to hit the target Give numerical answers accurate to two decimal places What is the time of ight if re the cannon at the smaller of the two angles Give a numerical answer accurate to two decimal places Problem 2 Consider the function fI7 y sinry2 Find the partial derivatives fag7 fy7 f 7 fgcy fygc and fyyl Problem 3 A tank in the shape of a right circular cylinder is measured to have a radius of 5 feet and a height of 10 feet If there is a pos sible error of ill feet in these measurements7 use increments to estimate the maximum possible error in the calculated volume of the tank and the maximum percentage error in the calculated volumel Problem 4 Let 2 fzy 12y my where z t2 and y 5t Find dzdt in the following two ways A Express 2 explicitly as a function of t and differentiate Bi Use the Chain Rule for partial derivatives7 expressing your nal answer as a function of ti Problem 5 Consider the function ay 12f my A Find the directional derivative of f at the point 1327 1 in the direction of the vector 74i 7 Sji B In what direction should you go from P to get the greatest rate of change in f What is this maximum rate of change Problem 6 Find the critical points of the function 40 pts 1 1 ay gang y2zy 1 Classify each of the critical points as a relative maximum7 relative minimum7 or a saddle pointi EXAM Exam 1 Math 2350705 Fall 2008 Wednesday October 8 2008 Write all of your answers on separate sheets of paper You can keep the exam questions when you leave You may leave when nished You must show enough work to justify your answers Unless otherwise instructed give exact answers not approximations elgl not 1414 This exam has 6 problems There are 160 points total Good luckl

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