To find: \(\lim\limits_{\text x \to0}\cfrac{tan\,3\text x-2\text x}{3\text x-sin^2\text x} \)
\(\lim\limits_{\text x \to0}\cfrac{tan\,3\text x-2\text x}{3\text x-sin^2\text x} \)
Dividing numerator and denominator by x:
We know,
Therefore,
\(=\cfrac13\)
Hence , the value of \(\lim\limits_{\text x \to0}\cfrac{tan\,3\text x-2\text x}{3\text x-sin^2\text x} \) \(=\cfrac13\)