Consider the function z= f(x, y) = x+5xy. (a) Find f(2, 1). z=f(2, 1) 18 (b)...

 

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Consider the function z= f(x, y) = x+5xy. (a) Find f(2, 1). z=f(2, 1) 18 (b) Find a function g(x, y, z) whose level zero set is equal to the graph of z = f(x, y) and such that the coefficient of z in g(x, y, z) is 1. The level set g(x, y, z) = = 0 is the same as the graph of z = f(x, y). (c) Find the gradient of g. Write your answer as a row vector of the general form (a, b, c). Vg(x, y, z) = (d) Use Vg to find a vector n perpendicular (or normal) to the graph of z = f(x, y) at the point (2, 1, 18). Write your answer as a row vector of the general form (a, b, c). F = (e) Find an equation for the tangent plane to z = f(x, y) at the point (2, 1, 18). Enter your answer as an equation. Consider the function z= f(x, y) = x+5xy. (a) Find f(2, 1). z=f(2, 1) 18 (b) Find a function g(x, y, z) whose level zero set is equal to the graph of z = f(x, y) and such that the coefficient of z in g(x, y, z) is 1. The level set g(x, y, z) = = 0 is the same as the graph of z = f(x, y). (c) Find the gradient of g. Write your answer as a row vector of the general form (a, b, c). Vg(x, y, z) = (d) Use Vg to find a vector n perpendicular (or normal) to the graph of z = f(x, y) at the point (2, 1, 18). Write your answer as a row vector of the general form (a, b, c). F = (e) Find an equation for the tangent plane to z = f(x, y) at the point (2, 1, 18). Enter your answer as an equation.