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I have a doubt about using Two Path Test (for checking the continuity of multi variable functions ) in case of those functions which remain non homogenous even after substituting $y$ in terms of $x$ or vice-versa.

For example:
Even after substituting $y$ in terms of $x$, if $x$ is remaining in numerator or denominator and limit is to be found at $x$ tending to zero, then will it be correct to say that limit tends to $0$ and $\infty$ for both the cases respectively?

Can you please help me?

Thanks!

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  • $\begingroup$ What is your question? See if this helps. $\endgroup$
    – Gokul
    Sep 18, 2017 at 4:43
  • $\begingroup$ Even after substituting 'y' in terms of 'x, "x" is remaining in Numerator or denominator and limit is to be found at x tending to zero, then will it be correct to say that limit tends to "0" and "Infinity" for both the cases respectively? $\endgroup$
    – Jatin Khare
    Sep 18, 2017 at 4:51
  • $\begingroup$ Please add the same details in the question so that it is complete and clear. $\endgroup$
    – Gokul
    Sep 18, 2017 at 4:55
  • $\begingroup$ Ok, Thanks for the help $\endgroup$
    – Jatin Khare
    Sep 18, 2017 at 4:56

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