JEE Main Mathematics Question (2026) — Solution

Step-by-step solution

Numerator: _e( (ex) (e^2x) (e^ 10 x)) = _ k=1 ^ 10 _e( (e^kx)). Using (u) 1 + u^2 2 for small u, we get _e( (e^kx)) e^ 2k x^2 2 . Thus the numerator is x^2 2 _ k=1 ^ 10 e^ 2k = x^2 e^2(e^ 20 -1) 2(e^2-1) . Denominator: Using x 1 - x^2 2 , we have e^ 2 x e^2(1-x^2), so e^2 - e^ 2 x e^2 x^2. Therefore: _ x 0 = x^2 e^2(e^ 20 -1) 2(e^2-1) e^2 x^2 = e^ 20 -1 2(e^2-1) .