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