To find: \(\lim\limits_{\text x \to0}\cfrac{5\text x\,cos\,\text x+3\,sin\,\text x}{3\text x^2+tan\,\text x}\)
\(\lim\limits_{\text x \to0}\cfrac{5\text x\,cos\,\text x+3\,sin\,\text x}{3\text x^2+tan\,\text x}\)
Dividing numerator and denominator by x:
We know,
{∵ cos 0 = 1}
\(=\cfrac{5+3}{0+1}\)
\(=\cfrac81\)
= 8
Hence, the value of \(\lim\limits_{\text x \to0}\cfrac{5\text x\,cos\,\text x+3\,sin\,\text x}{3\text x^2+tan\,\text x}\) = 8