This is an MCQ-based quiz on **Continuity and Differentiability.**

This includes Continuity, Differentiability, Exponential, Logarithmic Functions, Logarithmic Differentiation, Derivatives of Functions in Parametric Forms, Second Order Derivative, and Mean Value Theorem.

Let f(x) = |sin x| Then

The value of c in Rolle’s theorem for the function f(x) = x³ – 3x in the interval [o, √3] is

The function f(x) = e|x| is

Continuous everywhere but not differentiable at x = 0

Continuous and differentiable everywhere

Not continuous at x = 0

None of these

For x ∈ R, f(x) = |log 2 – sin x| and g(x) =f(f(x)), then

If g is the inverse of a function f and f"(x) = 1 /(1+x^5), then g"(x) is equal to

If y = sec (tan^-1 x), then dy /dx at x = 1 is equal to

Continuous for every real x

Discontinuous only at x = 0

Discontinuous only at non-zero integral values of x

Continuous only at x = 0.

If sin y + e^-x *cos y = e, then dy/dx at (1, π) is equal to

The derivative of y = (1 – x) (2 – x)…. (n – x) at x = 1 is equal to

If y = (1 + x) (1 + x²) (1 + x^4) …….. (1 + x^2n), then the value of dy/dx at x = 0 is

If f(x) = 5x / (1-x)^(2/3) + cos² (2x + 1), then f"(0) =

If y = ax² + b, then dy/dx at x = 2 is equal to ax

The set of points where the function f given by f (x) =| 2x – 1| sin x is differentiable is

R

R-1 / 2

(0, ∞)

None of these

The function f(x) = (4−x^2) / (4x−x^3) is

Discontinuous at only one point at x = 0

Discontinuous at exactly two points

Discontinuous at exactly three points

None of these