3xy ƒ(x,y) = 4x²+2y² a b) Find the domain of f. Show that the limit does not exist. lim f(x,y) (x,y) →(0,0)
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- If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?Find the limit (if it exists). If the limit does not exist, explain why. lim (xy+yz^2+xz^2/x^2+y^2+z^2) (x,y,z)--->(0,0,0)What does it mean for a function ƒ(x, y) to have limit L as (x, y) S (x0 , y0)?
- What does it mean for a function ƒ(x, y) to have limit L as (x, y) → (x0 , y0)? What are the basic properties of limits of functions of two independent variables?Show limit (x,y) -> (0,0) f(x,y) is invalidLet f(x, y) = xy /(x 2 + y2). Show that f(x, y) approaches zero along the x- and y-axes. Then prove that lim f(x, y) does not exist by (x,y) (0,0)showing that the limit along the line y =xis nonzero.
- Find the solution of the limit using polar coordinate system. Lim (x,y)->(0,0)√x^2+y^2/x^2+y^2Evaluate the limit: lim y-> 0 (1-cos 2y)/ (1- cos 4y)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.