JEE Main 2021 — Continuity and Differentiability Questions with Solutions

Let f   :   R → R be a function defined as f x = sin ( a + 1 ) x + sin 2 x 2 x , if   x < 0 b…

Let α ∈ R be such that the function f x = cos - 1 1 - x 2 sin - 1 1 - x x - x 3 , x ≠ 0 α , x = 0…

If the function f x = 1 x log e 1 + x a 1 - x   b                   &…

Let f   :   R → R satisfy the equation f ( x + y ) = f ( x ) · f ( y ) for all x , y ∈ R and…

Let [ t ] denote the greatest integer less than or equal to t . Let f ( x ) = x - [ x ] ,   g ( x ) = 1 - x + [ x…

Let f : - π 4 , π 4 → R be defined as, f x = 1 + sin x 3 a sin x ,    - π 4 < x &#60…

If the function f x = cos ( sin x ) - cos x x 4 is continuous at each point in its domain and f 0 = 1 k , then k is ___…

Let a function g : 0 , 4 → R be defined as g x = max   t 3 - 6 t 2 + 9 t - 3 0 ≤ t ≤ x , 0 &#880…

Let f : R → R be defined as f x = x 3 ( 1 - cos 2 x ) 2 log e 1 + 2 x e - 2 x 1 - x e - x 2 ,    x &#88…

Consider the function f x = P x sin x - 2 ,   x ≠ 2 , and f x = 7 ,   x = 2 where P x is a polynomial s…