Consider the following functions: f(x, y) = /x - 1 f(x, y) = x ln(y2 - x) For ea

Question

Consider the following functions: f(x, y) = /x - 1 f(x, y) = x ln(y2 - x) For each function, evaluate f(3, 2) and find and sketch the domain of each function. Find equations for the level curves of the given function for c = 2 and 4, and sketch the contour map for the function: f(x, y) = x + (y - 2)2/x Show that the following limit does not exist: Consider the function: f(x, y)= 3x/y + xy2. Use the limit definition to find fy(x, y). Hint: [f(x) + g(x)] = f(x) + g(x) Consider the function: f(x, y) = x4y + ln(y - x2) Find the first partials, fx(x, y) and fx(x, y). Show that the second partials. f infinity (x, y) and fyx (x, y) are equal.

Explanation / Answer

2)

set z = 2

2 = (x) + (y-x)^2 / x

x^2 + (y-2)^2 -2x = 0

(x-1)^2 + (y-2 )^2 = 1

circle with centre (1,2) and radius = 1

set z = 4

4 = (x) + (y-x)^2 / x

x^2 + (y-2)^2 -4x = 0

(x-2)^2 + (y-2 )^2 = 4

circle with centre (2,2) and radius = 2

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