Recent questions and answers in Calculus

A function $f(x)=1-x^2+x^3$ is defined in the closed interval $[-1,1]$. The value of $x$, in the open interval $(-1,1)$ for which the mean value theorem is satisfied, is$...

The value of $$\lim_{x\rightarrow \infty }(1 +\tfrac{1}{x})^{x}$$ is$\text{ln }2$$1.0$$e$$\infty$

As $x$ varies from $-1$ to $+3$, which one of the following describes the behaviour of the function $f(x)=x^{3}-3x^{2}+1?$$f(x)$ increases monotonically.$f(x)$ increases,...

The minimum value of the function $f(x)=\frac{1}{3} x(x^2-3)$ in the interval $-100≤x≤100$ occurs at $x =$ ________.

Consider a differentiable function $f(x)$ on the set of real numbers, such that $f(-1)=0$ and $ \mid f’(x) \mid \leq 2.$ Given these conditions, which one of the followin...

Given the following statements about a function $f: \Bbb R \rightarrow \Bbb R$, select the right option:P: If $f(x)$ is continuous at $x = x_0$ then it is also different...

$\lim _{x \rightarrow 0} \frac{x\left(e^{x}-1\right)+2(\cos x-1)}{x(1-\cos x)}$ is

In the Taylor series expansion of $\exp (x)+\sin (x)$ about the point $x=\pi$, the coefficient of $(x-\pi)^{2}$ is$\exp (\pi)$$0.5 \exp (\pi)$$\exp (\pi)+1$$\exp (\pi)-1$

The value of the integral $\iint_R \text{xy dx dy}$ over the region $R$, given in the figure, __________ is (rounded off to the nearest integer).