Question

Question 2. Comsider fcn log(2 - 2) (x2 + y2) (e) Find the level set of f which has value "height") wo 0, and describe it in words and set notation. Confirm that the point (2, 2, 1) is on this level surface, and that Vf(2,2, 1) is perpendicular to this surface. (f) Using cylindrical and spherical coordinates find feyl(p,9,2) and fsm(r, θ, φ). (g) Express the cartesian point (V3,-v3,-v/2) in cylindrical and spherical coordinates. Use your answers to directly evaluate the value of your functions foyl and fsph at the point a, and verify that the calculated values are the same.

Answer 1

This problem is from multivariate calculus.

2-Z 2 2 -o 2 og Ca-

So, level e 乙= ie S lies on the plane z-1. Cleaet

キy 7(午 2--2 2 ay 1(干

6Y 訇 which. Poiab in the tues panpendicula,右S.

2- P An AB

ib In spherical cemd:natu (n 8, +an 3 2- 3 3

6 yh 2 2-442

SP эт 3 Lt (2.h翠翠)

dspk Sun sPh So,we Ano thaț both same calcatedwolus at '