JEE Main 2022 — Limits Questions with Solutions

Let f : ℝ → ℝ be a function defined as f x = a sin π x 2 + 2 - x , a ∈ ℝ , where t i…

If lim x → 0 α e x + β e - x + γ sin x x sin 2 x = 2 3 , where α , β , γ ∈ R…

Let f x be a polynomial function such that f x + f ' x + f ' ' x = x 5 + 64 . Then, the value of lim x → 1 f x x…

Let t denote the greatest integer ≤ t and t denote the fractional part of t . Then integral value of α for w…

If lim x → 1 sin 3 x 2 - 4 x + 1 - x 2 + 1 2 x 3 - 7 x 2 + a x + b = - 2 , then the value of a - b is equal to

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

The value of lim x → 1 x 2 - 1 sin 2 π x x 4 - 2 x 3 + 2 x - 1 is equal to:

lim x → 1 2 sin cos - 1 x - x 1 - tan cos - 1 x is equal to

Let β = lim x → 0 α x - e 3 x - 1 α x e 3 x - 1 for some α ∈ ℝ . Then the value o…

lim x → π 2 tan 2 x 2 sin 2 x + 3 sin x + 4 1 2 - sin 2 x + 6 sin x + 2 1 2 is equal to