question starts at let. than one variable. Let f:R? → R3 be the function given by...

Question

Question

question starts at let.
than one variable. Let f:R? → R3 be the function given by f(x, y) = (cos(x3 - y2), sin(y2 – x), e3x2-x-2y). (a) Let P be a po

Answer 1

Answer #1

Son (ته 25 ,(sin ( x ,(12)وها ) = ( ر )4 Linear approximat at P =(1,1) - (ورد) وما (1-x) (ر )م 2 + (2-3) دما (9-1) (x2)دم ۵۰

) (b) 3x-2-24 = Linear Approscination f(a) around (1,1) (1, 2y-x-1, 5x-2y-2) g=(xyz, z log(ita-y-)) gof (cos(x²-yl), sin (9-x

!! PLEASE VOTE THUMBS UP !!

Answer 2

Similar Homework Help Questions

(1) (Definition and short answer — no justification needed) (a) Let f:R → R", and let...

(1) (Definition and short answer — no justification needed) (a) Let f:R → R", and let p ER". Define carefully what it means for the function f to be differentiable at p. (b) Given a linear transformation T : R" + R", explain briefly how to form its representing matrix (T). If you know the matrix (T), how can you compute T(v) for a vector v € R"? 1 and let S be the linear (c) Let T be the...
(1 point) Let f:R → R'be the linear transformation defined by T 4 -5 51 f(T)...

(1 point) Let f:R → R'be the linear transformation defined by T 4 -5 51 f(T) = -1 2 - 5 . | -4 0 3 Let B = {(-2,-1, 1), (-2, -2,1),(-1,-1,0)}, C = {{-2, -1, 1), (2,0, -1),(-1,1,0)}, be two different bases for R3. Find the matrix f for f relative to the basis B in the domain and C in the codomain. IT 3
1. Let f:R → R be the function defined as: 32 0 if x is rational...

1. Let f:R → R be the function defined as: 32 0 if x is rational if x is irrational Prove that lim -70 f(x) = 0. Prove that limc f(x) does not exist for every real number c + 0. 2. Let f:R + R be a continuous function such that f(0) = 0 and f(2) = 0. Prove that there exists a real number c such that f(c+1) = f(c). 3 Let f. (a,b) R be a function...

Question 5, Let ơ (u, v) : R2- R3 be a smooth function (not necessarily a surface patch). Let E O...

please be as detailed as possible Question 5, Let ơ (u, v) : R2- R3 be a smooth function (not necessarily a surface patch). Let E Ou .Ou, F-Ou . συ and G Oy .Oy. Show that the following equalities hold: (Here D denotes total derivative.) Question 5, Let ơ (u, v) : R2- R3 be a smooth function (not necessarily a surface patch). Let E Ou .Ou, F-Ou . συ and G Oy .Oy. Show that the following equalities...
(1) Let G(,y, z) = (x,y, z). Show that there exists no vector field A : R3 -> R3 such that curl(A) Hint: compute its...

(1) Let G(,y, z) = (x,y, z). Show that there exists no vector field A : R3 -> R3 such that curl(A) Hint: compute its divergence G. (2) Let H R3 -> R3 be given as H(x,y, z) = (1,2,3). Find a vector potential A : R3 -> R3 such that curl(A) smooth function = H. Show that if A is a vector potential for H, then so is A+ Vf, for any f : R5 -> R (3) Let...
(2) Consider the function f given by f:R R f(a)1 2 (a) Determine the domain D...

(2) Consider the function f given by f:R R f(a)1 2 (a) Determine the domain D and range R of the function f. (b) Show that f is not one to one on D. (c) Let ç D be a subset of the domain of f such that for all x ? S, 0 and the function is one to one. Find such a set S. (d) For the set S given in Part (c), find f (x) (e) Determine...

5. (7 points) Let f: R3 → R be the function f(x,y,z) = x2 + y2...

5. (7 points) Let f: R3 → R be the function f(x,y,z) = x2 + y2 +3(2-1)2 Let EC R3 be the closed half-ball E = {(x, y, z) e R$: x² + y2 +< 9 and 2 >0}. Find all the points (x, y, z) at which f attains its global maximum and minimum on E.
3. Let f RR2 and g RR2 be given by 2x1323 u1u2 T3 a) Write down the derivative matrices g' (u) an...

show all steps, please. 3. Let f RR2 and g RR2 be given by 2x1323 u1u2 T3 a) Write down the derivative matrices g' (u) and f'(a) and use the chain rule to find the derivative matrix (g o f)'(x); b) Are the entries of the new function (go f)(x) a linear or nonlinear function of ? 1 3 marks mark c) How do you understand the statement "(Df) (x) is a linear function" in Section 4.1 of the Class...
Problem 3 (12 points): Let D be a bounded domain in R" with smooth boundary. Suppose that K(x, y) is a Green's function for the Neumann . For each x E D, the function y H K(x, y) is a smooth...

Problem 3 (12 points): Let D be a bounded domain in R" with smooth boundary. Suppose that K(x, y) is a Green's function for the Neumann . For each x E D, the function y H K(x, y) is a smooth harmonic For each x E D, the normal derivative of the function y K(x, y) . For each z e D, the function y K(x,y)-Г(z-y) is smooth near problem. This means the following: function on D(r satisfies (VyK(x, y).v(b))-arefor...

(1 point) Let f: R3 R3 be the linear transformation defined by f(3) = [ 2...

(1 point) Let f: R3 R3 be the linear transformation defined by f(3) = [ 2 1 1-4 -2 -57 -5 -4 7. 0 -2 Let B C = = {(2,1, -1),(-2,-2,1),(-1, -2, 1)}, {(-1,1,1),(1, -2, -1),(-1,3, 2)}, be two different bases for R. Find the matrix (fls for f relative to the basis B in the domain and C in the codomain. [] =