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Consider the function f : R2 → R given by f(x, y) = xy³ + ye*-2. (a) For each of the following equations, determine whether it is right or wrong. fx(x, y) = y³ + ye*-2 • fy(x, y) = 3xy² + e*-2 * fxx(x, y) = ye*-2 fxy(x, y) = 3y² + ye*-2 • fyx (x, y) = 3y² + e*-2 • fyy(x, y) = 6x (b) The tangent plane to the graph of z = f(x, y) at the point (2, 1, 3) can be described by the equation x + y - z =

Consider the function f : R2 → R given by f(x, y) = xy³ + ye*-2. (a) For each of the following equations, determine whether it is right or wrong. fx(x, y) = y³ + ye*-2 • fy(x, y) = 3xy² + e*-2 * fxx(x, y) = ye*-2 fxy(x, y) = 3y² + ye*-2 • fyx (x, y) = 3y² + e*-2 • fyy(x, y) = 6x (b) The tangent plane to the graph of z = f(x, y) at the point (2, 1, 3) can be described by the equation x + y - z =

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the function f : R? → R given by f(x, y) = xy³ + ye*-2. (a) For each of the following equations, determine whether it is right or wrong. • fx(x, y) = y³ + ye*-2 • | fy(x, y) = 3xy² + e*-2 • fxx(x, y) = ye*-2 %3D • fxy(x, y) = 3y² + ye*-2 * fyx (x, y) = 3y² + e*-2 • fyy(x, y) = 6x (b) The tangent plane to the graph of z = f(x, y) at the point (2, 1, 3) can be described by the equation x + у Z = (c) Using the linear approximation of f(x, y) near (x, y) = (2, 1) tells us that f(1.99, 1.01) is approximately Please enter your answer as a decimal. (d) The most positive rate of change of f(x, y) at the point (x, y) = (2, 1) is in the direction of the vector (2, fe is equal to ds (e) If x = s2 – 2t² and y = s + t, then at the point (s, t) = (2, –1),
Transcribed Image Text:Consider the function f : R? → R given by f(x, y) = xy³ + ye*-2. (a) For each of the following equations, determine whether it is right or wrong. • fx(x, y) = y³ + ye*-2 • | fy(x, y) = 3xy² + e*-2 • fxx(x, y) = ye*-2 %3D • fxy(x, y) = 3y² + ye*-2 * fyx (x, y) = 3y² + e*-2 • fyy(x, y) = 6x (b) The tangent plane to the graph of z = f(x, y) at the point (2, 1, 3) can be described by the equation x + у Z = (c) Using the linear approximation of f(x, y) near (x, y) = (2, 1) tells us that f(1.99, 1.01) is approximately Please enter your answer as a decimal. (d) The most positive rate of change of f(x, y) at the point (x, y) = (2, 1) is in the direction of the vector (2, fe is equal to ds (e) If x = s2 – 2t² and y = s + t, then at the point (s, t) = (2, –1),
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