Evaluate the following limit : lim(x→0) (x cos x + 2 sin x)/(x^2+ tan x)

Question

Evaluate the following limit : \(\lim\limits_{\text x \to0}\cfrac{\text x\,cos\,\text x+2sin\,\text x}{\text x^2+tan\,\text x}\)

lim(x→0) (x cos x + 2 sin x)/(x²+ tan x)

Answer 1

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