Continuity And Differentiability Mock Tests

If f(x) = x² sin(1/x) for x ≠ 0 and f(0) = 0, then f is at x = 0:

If y = sin⁻¹(2x√(1 − x²)), then dy/dx equals:

The derivative of sin⁻¹(2x√(1 − x²)) with respect to x, where −1/√2 < x < 1/√2, is:

The derivative of sin⁻¹(2x/(1 + x²)) with respect to tan⁻¹x, where x > 0, x ≠ 1, is:

The function f(x) = |x − 1| is not differentiable at:

If y = eˣ · sin(x), then dy/dx is:

The derivative of sin⁻¹(2x√(1 − x²)) with respect to cos⁻¹(1 − 2x²), where 0 < x < 1/√2, is:

The function f : R → R defined by f(x) = [x], where [x] is the greatest integer ≤ x, is: