Let f : R2 + R be defined by f(x,y) = |xy|e-(z?+y?). Evaluate SR2 f, if...
Let f: R2 + R be defined by f(x, y) = xyle=(22+y?). Evaluate Sr2 f, if it exists
Let f:R2→R be defined by f(x,y) =|xy|e−(x2+y2). Evaluate ∫R2f, if it exists Let f : R2 + R be defined by f(L,y) = [tyle=(3++y?). Evaluate Sir2 f, if it exists
5. Let f : R2 + R be defined by f(x,y) = xyle=(x2+zº). Evaluate Sr2 f, if it exists (8 points).
(2) Let f(z, y)-xy +x-y be defined on the closed disk {(z, y) E R2 : z? + y2 < 4} of radius 2. (a) Find the maximu and minimu of Duf at (0,0) over all unit vectors u. (b) Find the maximum and minimum of Duf over all points in the disk(,y) E R2 r2 + y2 < 4} and all unit vectors u. (llint. Think of IvJF as a function ofェand y in the disk.)
Let f: R2 + R be defined by f(x, y) = xyle=(22+v?). Evaluate Sg2 f, if it exists
Let f : R2 + R be defined by f(L,y) = |kyle=(2²+y?). Evaluate /ik2 f, if it exists
1(a) Let f : R2 → R b constant M > 0 such that livf(x,y)|| (0.0)-0. Assume that there exists a e continuously differentiable, with Mv/r2 + уг, for all (z. y) E R2 If(x,y)| 〈 M(x2 + y2)· for all (a·y) E R2 Prove that: 1(a) Let f : R2 → R b constant M > 0 such that livf(x,y)|| (0.0)-0. Assume that there exists a e continuously differentiable, with Mv/r2 + уг, for all (z. y) E R2...
Let A C R and fA: R2-given by 1 if (x, y) E A 0 if (r, y) A Ar, y): a)Prove that fAis continuosin int(A)Uert(A) and f is dicontinuos in cl(A) b)Draw fA a) A = B2 (0) . b) A = {(x,y) | xy = 0} . c) A = {(z, y) | y E Q)
Let X, Y E Mn (R). Prove that XY = XY_if and only if there exists an invertible matrix Z so that X = Z In and Y = Z1 + In. Hint: the trace is not involve at all in this problem _
Let f(x,y,z) = xy + z-5,x=r +2s, y = 2r - sec(s), z = s Then I is: ar a. r - sec(s) b. sec(s) c. r+s+sec(s) d. 4r + 4s - sec(s) a. b. C. Given zº – xy + y2 + y2 = 2 and z is a differentiable function in x and y. Then at (1,1,1) is: дх a. 0 b. 1 c. d. e. None of the above o a. o b. ♡ C. o d.