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

Question

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

lim(x→0) (2x - sin x)/(tan x + x)

Answer 1

To find: \(\lim\limits_{\text x \to0}\cfrac{2\text x-sin\,\text x}{tan\,\text x+\text x}\) 

\(\lim\limits_{\text x \to0}\cfrac{2\text x-sin\,\text x}{tan\,\text x+\text x}\)

Dividing numerator and denominator by x:

We know,

Therefore,

Hence, the value of \(\lim\limits_{\text x \to0}\cfrac{2\text x-sin\,\text x}{tan\,\text x+\text x}\) = \(\cfrac12\)