Continuity and ...

If f (x) = 2x and g (x) = \(\frac{x^2}{2}\) + 1, then which of the following can be a discontinuous function

The function f (x) = \(\frac{4 - x^2}{4x - x^3}\) is

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

The function f (x) = cot x is discontinuous on the set

The function f(x) = \(e^{|x|}\) is

If f(x) = \(x^2 sin \frac{1}{x}\), where x \(\neq \) 0, then the value of the function f at x = 0, so that the function is continuous at x = 0, is

If f(x) = \(\begin{cases} mx + 1, & \quad \text{if } x \leq \frac{\pi}{2}\\ sin x + n, & \quad \text{if } x > \frac{\pi}{2} \end{cases}\), is continuous at x = \(\frac{\pi}{2}\), then

Let f (x) = |sin x|. Then

If y = log \((\frac{1 - x^2}{1 + x^2})\), then \(\frac{dy}{dx}\) is equal to

If y = \(\sqrt{sin x + y}\), then \(\frac{dy}{dx}\) is equal to

The derivative of \(cos^{–1} (2x^2  – 1)\) w.r.t. \(cos^{–1}x\) is

If x = \(t^2\), y = \(t^3\), then \(\frac{d^2y}{dx^2}\) is

The value of c in Rolle’s theorem for the function f (x) = \(x^3\) – 3x in the interval [0, \(\sqrt 3\)] is

For the function f (x) = x + \(\frac{1}{x}\), x \(\in\) [1, 3], the value of c for mean value theorem is

Which of the following statements is true

Let h(x) = min{x, \(x^2\)}, for every real number of x. Then

If f(x) = |x−2|, then

In order that the function f(x) = \((x+1)^{1/x}\) is continuous at x = 0, f(0) must be defined as

At which points the function f(x) = \(\frac{x}{[x]}\), where [.] is greatest integer function, is discontinuous

If f(x) = |x - b|, then function