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Let g(x,y) = (x^(2)y)/(x^(4) + y^(2)) fo...

Let `g(x,y) = (x^(2)y)/(x^(4) + y^(2))` for (x,y) `ne` (0,0) and f(0,0)=0.
(i) Show that `lim_((x,y) to (0,0)) g(x,y)=0` along every line `y=mx, m in R`.
(ii) Show that `lim_((x,y) to (0,0)) g(x,y) = k/(1+k^(2))`, along every parabola `y=kx^(2), k in R{0}`.

Text Solution

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The correct Answer is:
`R //{0}`
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