tmt1
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I have
$$\lim_{{(x, y)}\to{(0, 0)}} \frac{x^4 - y^4}{x^4 + x^2y^2 + y^4}$$
If I evaluate the limit along the x-axis, I get
$$\lim_{{(x, y)}\to{(0, 0)}} \frac{x^4 - y^4}{x^4 + x^2y^2 + y^4}$$
which evaluates to $1$.
If I evaluate the limit along the y-axis, I get
$$\lim_{{y}\to{0}} \frac{ - y^4}{ y^4}$$
which evaluates to $-1$.
Since the 2 limits are different, then the limit does not exist. Is this correct?
$$\lim_{{(x, y)}\to{(0, 0)}} \frac{x^4 - y^4}{x^4 + x^2y^2 + y^4}$$
If I evaluate the limit along the x-axis, I get
$$\lim_{{(x, y)}\to{(0, 0)}} \frac{x^4 - y^4}{x^4 + x^2y^2 + y^4}$$
which evaluates to $1$.
If I evaluate the limit along the y-axis, I get
$$\lim_{{y}\to{0}} \frac{ - y^4}{ y^4}$$
which evaluates to $-1$.
Since the 2 limits are different, then the limit does not exist. Is this correct?