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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
Let f : (- 1, 1) → R be a differentiable function with f(0) = – 1 and f"(0) = 1. Let g(x) = [f (2f(x) + 2)]². Then g"(0) =
If f: R → R is a function defined byf(x) = [x] cos ((2x-1) / 2)π, where [x] denotes the greatest integer function, then ‘f’ is
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
