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DANIEL

Cálculo 306/19/2024

Mostre que o limite não existe a)

Mostre que o limite não existe a) lim(x,y)(0,0)(3x2+2y2)\lim _{(x, y) \rightarrow(0,0)}\left(\frac{3}{x^{2}+2 y^{2}}\right) b) lim(x,y)(0.0)(x+yx+y2)\lim _{(x, y) \rightarrow(0.0)}\left(\frac{x+y}{x+y^{2}}\right) f) lim(x,y)(1,2)(xy2xy+2x2+y22x4y+5)\lim _{(x, y) \rightarrow(1,2)}\left(\frac{x y-2 x-y+2}{x^{2}+y^{2}-2 x-4 y+5}\right) c) lim(x,y)(0,0)(xy3x2+2y2)\lim _{(x, y) \rightarrow(0,0)}\left(\frac{x y}{3 x^{2}+2 y^{2}}\right) g) lim(x,y)(0,0)(3x2y32y52x5)\lim _{(x, y) \rightarrow(0,0)}\left(\frac{3 x^{2} y^{3}}{2 y^{5}-2 x^{5}}\right) d) lim(x,y)(0.0)(1x2y2x2y2)\lim _{(x, y) \rightarrow(0.0)}\left(\frac{1-x^{2}-y^{2}}{x^{2}-y^{2}}\right) i) lim(x,y,z)(0,0,0(x3+y3+z3xyz)\lim _{(x, y, z) \rightarrow(0,0,0}\left(\frac{x^{3}+y^{3}+z^{3}}{x y z}\right) e) lim(x,y)(0,0)(2x2y2x2+2y2)\lim _{(x, y) \rightarrow(0,0)}\left(\frac{2 x^{2}-y^{2}}{x^{2}+2 y^{2}}\right)

Mostre que o limite não existe
a) \( \lim _{(x, y) \rightarrow(0,0)}\left(\frac{3}{x^{2}+2 y^{2}}\right) \)
b) \( \lim _{(x, y) \rightarrow(0.0)}\left(\frac{x+y}{x+y^{2}}\right) \)
f) \( \lim _{(x, y) \rightarrow(1,2)}\left(\frac{x y-2 x-y+2}{x^{2}+y^{2}-2 x-4 y+5}\right) \)
c) \( \lim _{(x, y) \rightarrow(0,0)}\left(\frac{x y}{3 x^{2}+2 y^{2}}\right) \)
g) \( \lim _{(x, y) \rightarrow(0,0)}\left(\frac{3 x^{2} y^{3}}{2 y^{5}-2 x^{5}}\right) \)
d) \( \lim _{(x, y) \rightarrow(0.0)}\left(\frac{1-x^{2}-y^{2}}{x^{2}-y^{2}}\right) \)
i) \( \lim _{(x, y, z) \rightarrow(0,0,0}\left(\frac{x^{3}+y^{3}+z^{3}}{x y z}\right) \)
e) \( \lim _{(x, y) \rightarrow(0,0)}\left(\frac{2 x^{2}-y^{2}}{x^{2}+2 y^{2}}\right) \)
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