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# Short Calculus MAT 016C

UCD

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This 2 page Study Guide was uploaded by Otilia Murray I on Tuesday September 8, 2015. The Study Guide belongs to MAT 016C at University of California - Davis taught by Peter Malkin in Fall. Since its upload, it has received 108 views. For similar materials see /class/187338/mat-016c-university-of-california-davis in Mathematics (M) at University of California - Davis.

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Date Created: 09/08/15

SHORT CALCULUS Math 160 Sec 1 Fall 2008 Final Exam Study Guide Peter Malkin Below is a list of the sections covered by each question together with an exhaustive list of types of questions that I might ask on the nal exam for each question The list of types of questions are not given in any order 0 Sections Cil 04 7 Verify that an equation satis es a differential equation 7 Find the general solution of a differential equation using either straightforward integra tion the separation of variables technique or the linear rst order differential equation technique 7 Find a particular solution of a differential equation given initial conditions 7 Given a verbal description of an application of differential equations write down the differential equation 96 nd the general solution of the differential equation 96 nd the particular solution of the differential equation using intial conditions 96 and answer questions about the application using the solution of the differential equation 0 Sections 71 72 7 Find the midpoint of two points 7 Find the distance between two points 7 Find the equation of a sphere given sufficient information eigi center and radius or two endpoints of a diameter 7 Find the center and radius of a sphere from the equation of the sphere 7 Sketch the trace of a surface ie the intersection of a surface with a plane 7 Sketch a plane given by an equation 7 Sketch and or identify a quadric surface from the equation of the surface ellipsoid ellip tic parabloid hyperbolic parabloid elliptic cone hyperboloid of one sheet hyperboloid of two sheets i 0 Sections 73 7 Find the domain and range of a function and sketch the domain 7 Sketch the level curves of a given function or surface 7 Sketch a contour map of a function or surface 0 Sections 74 7 Find the rst order partial derivatives and second order partial derivatives of a function 7 Evaluate the rst order and or second order partial derivates of a function at a point 7 Find the slope of a surface 2 fz y at a point in the zdirection and y directioni 0 Sections 75 7 Find the critical points of a function SHORT CALCULUS Math 160 Sec 1 Fall 2008 Midterm exam 2 Study Guide Peter Malkin The structure of the midterm exam is as follows Below is a list of the sections covered by each question together with an exhaustive list of types of questions that I might ask on the midterm exam for each question The list of types of questions are not given in any order 0 Sections 73 7 Find the domain and range of a function and sketch the domain 7 Sketch the level curves of a given function or surface 7 Sketch a contour map of a function or surface 0 Sections 74 7 Find the rst order partial derivatives and second order partial derivatives of a function 7 Evaluate the rst order and or second order partial derivates of a function at a point 7 Find the slope of a surface 2 fz7 y at a point in the zdirection and y directioni 0 Sections 75 7 Find the critical points of a function 7 Classify the critical points of a function 0 Section 7 6 7 Find the minimum or maximum of a functions in several variables subject to one or two constraints using the Lagrange multiplier method 0 Sections 78 79 7 Find the partial integral of a function 7 Find a function given its partial derivatives 7 Evaluate a double integral 7 Draw the region of integration given a double integral 7 Change the order of integration of a double integral 7 Find the area of a region in 2dimensions by evaluating a double integral 7 Find the volume under a surface and above a region by evaluating a double integral 7 Find the average value of a function over a region by evaluating a double integrali

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