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Short Calculus

by: Otilia Murray I

Short Calculus MAT 016C

Otilia Murray I
GPA 3.88


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Class Notes
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This 2 page Class Notes was uploaded by Otilia Murray I on Tuesday September 8, 2015. The Class Notes belongs to MAT 016C at University of California - Davis taught by Staff in Fall. Since its upload, it has received 20 views. For similar materials see /class/187461/mat-016c-university-of-california-davis in Mathematics (M) at University of California - Davis.

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Date Created: 09/08/15
1 Math 16C02 Midterm Review Date of test Monday July 14 What will be covered Sections 31 047 and 71 76 will all be on the test Be sure to know how to verify that a function is a solution of a differential equation including by using implicit differentiation nd a particular solution of a differential equation given some initial data solve a differential equation using both separation of variables and an integrating factor formulate and solve exponential growth and decay as a differential equation7 as well as other application problems discussed in class and in section 04 plot points in 3 dimensions plot planes nd the traces of quadric surfaces and identify a quadric surface from its traces nd the distance and midpoint between two points in 3 dimensions nd the standard equation of a sphere7 and determine what the center and radius of a sphere differentiate between parallel and perpendicular planes see homework problems 137 147 197 20 in section 72 of the text This probably won7t be on the exam7 but I think its interesting enough to learn7 so I might throw a 2 pointer on there nd the domain and range of a function of 2 variables I cannot stress this enough come see me during of ce hours if you don7t understand what the domain and range refer to THIS WILL BE ON THE EXAM nd level curves and draw them nd the rst and second partial derivatives of a function nd and classify critical points by using the second partial derivatives test7 or by using some basic analysis see problems 267 307 and 51 in section 75 for examples of functions for which the second partials test fails7 but you can still determine whether the critical points are maxima or minima solve optimization problems using Lagrange multipliers This includes being able to identify the objective function to be optimized and the constraint func tion from a word problem H E0 00 r U 03 Practice Questions Find all relative extrema of ay 12 73x2y 7x24y2 using the second partials test Find all relative extrema of Way 9632 6962 7 81 using the second partials test Solve the following differential equations using any method a dyiylns dzi z b 1dy73 1 zdzi g 0 d ii 3 yd We 296 Verify that 6x2 7 2y2 C is a solution to the differential equation 3x 9 i 9 Find the zy 2 and z 1 traces of 2 2 y z 7 7 7 7 0 95 4 9 Make sure to label your axes and any intercepts What type of quadric surface is this Plot the plane z 7 3y 22 6 Classify this plane as parallel7 perpendicular or neither to the plane 74x 12y 7 82 10 Justify your answer


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