Evaluate the following limit : lim(x→0) (7x cos x - 3 sin x)/(4x + tan x)

Question

Evaluate the following limit : \(\lim\limits_{\text x \to 0}\cfrac{7\text x\,cos\,\text x-3sin\,\text x}{4\text x+tan\,\text x} \)

lim(x→0) (7x cos x - 3 sin x)/(4x + tan x)

Answer 1

To find: \(\lim\limits_{\text x \to 0}\cfrac{7\text x\,cos\,\text x-3sin\,\text x}{4\text x+tan\,\text x} \)

\(\lim\limits_{\text x \to 0}\cfrac{7\text x\,cos\,\text x-3sin\,\text x}{4\text x+tan\,\text x} \) 

Dividing numerator and denominator by x:

We know,

Therefore,

Hence, the value of \(\lim\limits_{\text x \to 0}\cfrac{7\text x\,cos\,\text x-3sin\,\text x}{4\text x+tan\,\text x} \) = \(\cfrac45\)