Continuity and Differentiability

JEE Main Mathematics · 5 questions

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• For the function f(x)=e^sin |x|-|x|, x ∈ R, consider the following statements: Statement I: f is differentiable for all x ∈ R.…20268 April, Shift 2 · Q13
• Let f(x)= {x^3+8; x<0, x^2-4; x ≥ 0,} and g(x)= {(x-8)^1 / 3; x<0, (x+4)^1 / 2; x ≥ 0.} Then the number of points, where the…20266 April, Shift 2 · Q25
• Let f(x)= {e^x-1, x<0; x^2-5 x+6, x ≥ 0} and g(x)=f(|x|)+|f(x)|. If the number of points where g is not continuous and is not…20264 April, Shift 2 · Q22
• The number of points, at which the function f(x)= max {6 x, 2+3 x^2}+|x-1| cos |x^2-1/4|, x ∈(-π, π), is not differentiable, is…20264 April, Shift 1 · Q25
• The number of points in the interval [2,4], at which the function f(x)=[x^2-x-1/2], where [•] denotes the greatest integer…20262 April, Shift 2 · Q25