the limit lim(x,y,z)→(0,0,0)[xy+xz+yz]/[x2+y2+z2]
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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) ?Let f(x, y) =x2(y−1)x4+(y−1)2. Determine the existence of limit lim(x,y)→(0,1)f(x, y).Let f(x,y,z)=x^2+4y^2+2z^2. Does the limit lim_(0,0,0)f(x,y,z) exist? If so, use generalized to 3 dimension to show that this is the limit.
- Find the limits lim f(x, y), (x,y)→(1,π) lim g(x, y), (x,y)→(0,0) for the functions f(x,y) = y/x − sin(xy), g(x,y) = (xy + 2y^3) / (x^2 + y^2)Let 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.Let f(x,y)=(x−y)/(x^2+3xy−4y^2). Find the limit lim(x,y)→(2,2) f(x,y).
- Evaluate the limit limn→∞ ∑ n i=1 f(ci ) Δxi over the region bounded by the graphs of the equations.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)Find the solution of the limit using polar coordinate system. Lim (x,y)->(0,0)√x^2+y^2/x^2+y^2
- Prove that the limit of xy[(x^2 - y^2)/(x^2 + y^2)] is zero as (x, y) goes to (0,0)Let f (x, y) = xy/(x2 + y2). Show that f (x, y) approaches zeroalong the x- and y-axes. Then prove that lim (x,y)→(0,0)f (x, y) does not exist by showing that the limit along the line y = x is nonzero.Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim (x, y, z)→(0, 0, 0) yz x2 + 4y2 + 4z2
