
Find the linearization L(x,y) of the function f(x,y)= e 3x cos (y) at the points (0,0) and RIN The linearization at (0,0) is L(x,y)= (Type an exact answer, using a as needed.) The linearization at 0. is L(x,y)= 0 (Type an exact answer, using a as needed.)
DUE DATE: 23 MARCH 2020 1 1. Let f(x,y) = (x, y) + (0,0) 0. (x, y) = (0,0) evaluate lim(x,y)=(4,3) [5] 2r + 8y 2. Show that lim does not exist. [10] (*.w)-(2,-1) 2.ry + 2 3. Find the first and second partial derivatives of f(x,y) = tan-'(x + 2y). [16] 4. If z is implicitly defined as a function of x and y by I?+y2 + 2 = 1, show az Əz that +y=z [14] ar ду 5....
1. Find grad f from the following functions 0) f =(x - 1) (4-1) (ii)f=2x2 + 5y2 (iii) f = x + ys v)f=(x2+ y2) (x2-y)
3. (1,7) (0,0) { 0 f (x, y) = 23r²ty (z,y) = (0,0) (a) (10 pts) Evaluate the limit, or use a two-path test to show that it does not exist: lim f(x,y). (sy)(0,0) Math 250 Final Exam, CSU Northridge (b) (4 pts) Is f(x,y) continuous? Explain why or why not. 4. (17 pts) Use Lagrange multipliers to find the absolute maximum and absolute min- imum of f(x,y) = ry", subject to the constraint 3x² + y = 12. 5/12/20
3. Find lim f(,y) if it exists, and determine if f is continuous at (0,0. (x,y)--(0,0) (a) f(1,y) = (b) f(x,y) = { 0 1-y if(x, y) + (0,0) if(x,y) = (0,0) 4. Find y (a) 3.c- 5xy + tan xy = 0. (b) In y + sin(x - y) = 1.
Let f(x,y)= (x + y2 0 you find a 8 >0 such that f(x,y)-f(0,0) <0.01 x,y) = (0,0) (15 marks) whenever
Find the value of b for 2xº + 2xy2 + 3x² + 3y2 - if (x, y) = (0,0) 2. a) Let f(x, y) = x + y if (x, y) = (0,0) which fis continuous at all the points in R2. if (x, y) + (0 -2) Is f continuous at (0, -2)? 1 2x + xy b) Let f(x, y) = 3x² + (2 + y)? 12 Explain! if (x, y) = (0, -2)
Exercice 2 (5pts) Let f given by f(x, y) Isinyif (x, y) (0,0) and f(0,0) 0 1V224 1. Is f continuous at (0,0). 2. Compute the partial derivatives of f at any (x, y) E R2. Are the partial derivatives continuous (0,0). at (0,0) (0,0) and 3. Compute the second derivatives 4. Compute the linear approzimant of f at (0,0).
Exercice 2 (5pts) Let f given by f(x, y) Isinyif (x, y) (0,0) and f(0,0) 0 1V224 1. Is f...
5) Determine and state the work done by the vactor ficld over the given pathin each situation A) F (3x -y,2x). Move from (0,0) to (3,6) then from (3,6) to (90 ByF = (6x2-6xy. 4-3x 2) Move from (00) to144) then tom (4,4) to (62). C) f-(3у, 4x) Move from (0.0) to (6,3) then from (63) to 406) 6m from (0,6) back to (0,0)
5) Determine and state the work done by the vactor ficld over the given pathin each...
Find f1(x) if f(x) = 3x - 4 이 0