JEE Main Mathematics — Continuity and Differentiability Previous-Year Questions

Let [·] denote the greatest integer function, and let f(x)= \√(2) x, x² \. Let S= \x (-2,2) . : the function g(x)=|x| […

Let α, β R be such that the function f(x)= cases2 α (x²-2 )+2 β x &, x be differentiable at all x R. Then 34(α+β) is eq…

Let f(x)= θ → ₀ ( π x-x ⁽⁽²⁾/⁽θ⁾ⁱght⁾ (x-1)1+x ⁽⁽²⁾/⁽θ⁾ⁱght⁾(x-1) ), x R. Consider the following two statements : (I) f…

Let f(x) = cases (1)/(3), & x ≤ π/2 \ (b(1- x))/((π-2x)²), & x > π/2 cases. If f is continuous at x=π/2, then the value…

If f(x)= \arraycca|x|+x²-2( |x|)( |x|)x &, x ≠ 0 \ b &, x=0array . is continuous at x=0, then a+b is equal to

The number of points, at which the function f(x) = \6x, 2 + 3x² + |x - 1| | |x² - (1)/(4) | |, x (-π, π), is not differ…

If the function f(x)=ex (eⁿ x⁻x-1 )+ e( x+ x)-x x-x is continuous at x=0, then the value of f(0) is equal to

The number of points in the interval [2, 4], at which the function f(x) = [x² - x - (1)/(2) ], where [·] denotes the gr…

Let f(x) = cases x³ + 8 ; & x Then the number of points, where the function g ° f is discontinuous, is __________.

Let f(x)=cases ex⁻¹, & x<0 \ x²-5x+6, & x ≥ 0 cases and g(x)=f(|x|)+|f(x)|. If the number of points where g is not cont…