JEE Main 2024 — Continuity and Differentiability Questions with Solutions

If the function f x = 1 | x | , | x | ≥ 2 a x 2 + 2 b , | x | < 2 is differentiable on R , then 48 ( a + b ) is equal t…

Consider the function f : ( 0 , 2 ) → R defined by f ( x ) = x 2 + 2 x and the function g ( x ) defined by g x = min {…

Let f:(0, π) → R be a function given by f(x)= \arraycc ((8)/(7) )⁽ⁿ ⁸ x⁾/⁽ⁿ ⁷ x⁾, & 0 where a, b Z. If f is continuous…

For a, b>0, let f(x)= \arraycc ((a+1) x)+b xx, & x 0array . be a continous function at x=0. Then ba is equal to :

Let f: R → R be a function given by $f(x)=\left\{\begin{array}{ll} \frac{1-\cos 2 x}{x^2}, & x 0 \end{array}\right.$ wh…

Let f x = lim r → x 2 r 2 ( f ( r ) ) 2 - f ( x ) f ( r ) r 2 - x 2 - r 3 e f ( r ) r be differentiable in ( - ∞ , 0 )…

Let [t] denote the greatest integer less than or equal to t. Let f:[0, ∞) → R be a function defined by f(x)= [(x)/(2)+3…

Consider the function f : 0 , ∞ → R defined by f x = e − log e x . If m and n be respectively the number of points at w…

Let f:[-1,2] → R be given by f(x)=2 x²+x+ [x² ]-[x], where [t] denotes the greatest integer less than or equal to t. Th…

Let g x be a linear function and f x = g x , x ≤ 0 1 + x 2 + x 1 x , x > 0 , is continuous at x = 0 . If f ' 1 = f − 1…