JEE Main 2024 — Limits Questions with Solutions

If a = lim x → 0 1 + 1 + x 4 - 2 x 4 and b = lim x → 0 sin 2 x 2 - 1 + cos x , then the value of a b 3 is :

Let f : - π 2 , π 2 → R be a differentiable function such that f 0 = 1 2 , If lim x → 0 x ∫ 0 x f ( t ) d t e x 2 - 1 =…

Let f:(-∞, ∞)-\0 → R be a differentiable function such that fⁱme(1)= a → ∞ a² f ((1)/(a) ). Then a → ∞ (a(a+1))/(2) ⁻¹…

The value of x → ₀ 2 (1- x √( 2 x) [3] 3 x … … [10] 10 xx² ) is

Let the slope of the line 45 x + 5 y + 3 = 0 be 27 r 1 + 9 r 2 2 for some r 1 , r 2 ∈ R . Then lim x → 3 ∫ 3 x 8 t 2 3…

Let x denote the fractional part of x and f x = cos − 1 1 − x 2 sin − 1 1 − x x − x 3 , x ≠ 0 . If L and R respectively…

If α= x → ₀⁺ (e√⁽ⁿ x⁾-e√⁽x⁾√( x)-√(x) ) and β= x → ₀(1+ x)⁽¹⁾/⁽²⁾ x are the roots of the quadratic equation a x²+b x-e=…

Let a>0 be a root of the equation 2 x²+x-2=0. If x → 1a 16 (1- (2+x-2 x² ) )(1-a x)²=α+β √(17), where α, β Z, then α+β…

x → ₀ e-(1+2 x)⁽¹⁾/⁽² x⁾x is equal to

Let f : → R → 0 , ∞ be strictly increasing function such that lim x → ∞ f 7 x f x = 1 . Then, the value of lim x → ∞ f…