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Cal_C_test_2 - ii t,j I lzi L I Ji MA 201 Studv Guide for...

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ii.: t,j ! I lzi I L Ji 4,6t6 MA 201 Studv Guide for Test 2 You need to know: The graph of z = f (x,y) is a surface in 3-space' A fevel cLlrve is a set of points where f (x,y)= some constant k. Must be able to approach (a, b) from any direction, along any path, for /(r,.v) to have a limit at (a, b), must have limit at (a, b) to be continuous at (a, b)' A-Rule of thumb: ii t is given by a formula in elementary functions' then f is continuous wherever it is well-defined. , ..The Heart of Calculus Formula for functions of multiple variables: .{{I +;g) =./(i) + V.f .;6 (Okay, so you don't have to actually know this, but it sure looks nice.) rlMaximum rate of change of a function occurs in direction of the gradient' .$The gradieni vecior is perpendicular to level curves of the function. :f A continuous function on a closed, pounded set attains an absolute maximum and absoluie minimum on that set- . '' You need to be able to: Find partial derivatives - differentiate with respect to one variable while treating the other(s) as constants. Recognize and interpret both ways of writing partial derivatives' :.,.Use ilairaut's Theoiem {and rernember to say that you are using it and, if necessary, justifY its use) Find the equation of the plane tangent to the graph of z = -f (x,.:-') at ('tto'"1'o ) ' ,,. .Oraw a tree cliagram(if you need it) and use the chain rule to find needed partials' Find the gradient vector for a function. Find the directional derivative of /(t) at io in the direction of it ' Find the maximum rate of change of a function at a point, and the direction in which it occurs.
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