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- Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim (x, y, z)→(0, 0, 0) yz x2 + 4y2 + 4z2Let y(t) be the solution of dy/dt = 0.3y(2 − y) with y(0) = 1. Determine limt→∞ y(t) without solving for y explicitly.Use the limit definition to show that the partial derivatives of F(x,y) = with respect to x and y are/aren’t the same any point(a,b). (i.e show that Fx(a,b) =/≠ Fy(a,b))
- Use the limit definition to calculate the derivative at z = a of the linear function k(z) = 5z + 16.A function h(x, y) is defined by h(x,y)=(x^2 y)/(〖7x〗^6+y^3 ). Verify the limit over h(x, y) exists at the origin along y = x^2? In either case write also the reason.Show that f(x,y) limit exists at (0,0) using epsilon-delta.