lim x → 0 x + 2 cos x 3 + 2 x + 2 cos x 2 + 3 sin x + 2 cos x x + 2 3 + 2 x + 2 2 + 3 sin x + 2 100 x is equal to

Step-by-step solution

Given, l i m x → 0 x + 2 c o s x 3 + 2 x + 2 c o s x 2 + 3 s i n x + 2 c o s x x + 2 3 + 2 x + 2 2 + 3 s i n x + 2 100 x Now by putting the value of limit we can see it is in form 1 ∞ Now we know that, lim x → 0 f x g x when is in form of 1 ∞ , we can write this as e lim x → 0 f x - 1 g x Now using the above rule we get, = e lim x → 0 x + 2 cos x 3 + 2 x + 2 cos x 2 + 3 sin x + 2 cos x x + 2 3 + 2 x + 2 2 + 3 sin x + 2 - 1 × 100 x = e lim x → 0 100 x x + 2 cos x 3 + 2