10 Question MCQ (including Assertion)

A function is defined as \(f(x)=x^2 \sin \left(\frac{1}{x}\right)\) for \(x \neq 0\) and \(f(0)=0\). This function is:

The temperature of a cup of coffee, \(T(t)\), over time \(t\) is modeled by a function. Which of the following statements best describes why \(T(t)\) must be a continuous function?

The value of c in Rolle's Theorem for the function \(\mathrm{f}(\mathrm{x})=e^x \sin x\), \(x \in[0, \pi]\) is

The derivative of the function \(f(x)=e^x\) is \(e^x\). This unique property means that the value of the function is always equal to:

The function given by \(\mathrm{f}(\mathrm{x})=\tan \mathrm{x}\) is discontinuous on the set

Assertion (A): If a car moves with constant velocity, its acceleration is zero.
Reason (R): Acceleration is the second derivative of the position function, and the derivative of a constant (velocity) is zero.

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

A company's profit \(P(x)\) from selling \(x\) units is given by a differentiable function. What does the derivative \(P^{\prime}(x)\) represent in a business context?

The number of points at which the function \(\mathrm{f}(\mathrm{x})=\frac{1}{x-[x]}\) is not continuous is