5. Let f(x, y) = xln(x/y)+ xy² a. Calculate f and fx b. Determine the directional derivative off at the point (2, 2) in the direction of the vector a=i-2j c. Suppose that x = ste' and y=2se¹. Calculate af Ət d. Determine an equation for the tangent plane to the surface z = f(x, y) at the point (2, 2, 8) on the surface.

Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.2: Introduction To Conics: parabolas
Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.
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5. Let f(x, y) = xln(x/y)+ xy²
a. Calculate f and fx
b. Determine the directional derivative off at the point (2, 2) in the direction of the vector
a=i-2j
c. Suppose that x = ste' and y=2se¹. Calculate
af
Ət
d. Determine an equation for the tangent plane to the surface z = f(x, y) at the point (2, 2, 8) on
the surface.
Transcribed Image Text:5. Let f(x, y) = xln(x/y)+ xy² a. Calculate f and fx b. Determine the directional derivative off at the point (2, 2) in the direction of the vector a=i-2j c. Suppose that x = ste' and y=2se¹. Calculate af Ət d. Determine an equation for the tangent plane to the surface z = f(x, y) at the point (2, 2, 8) on the surface.
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