Recent questions and answers in Functions of Single Variable

Let\[f(x)=\left\{\begin{array}{cr}\pi+x, & -\pi \leq x<0, \\0, & 0 \leq x<\pi,\end{array}\right.\]with $f(x+2 \pi)=f(x)$. If $F(x)$ represents the Fourier series of $f(x)...

Assume that $f:[0,1] \rightarrow \mathbb{R}$ is continuous on $[0,1]$ and differentiable on $(0,1)$ such that $f(x+h)=f(x)+h f^{\prime}(x+\theta h)$ for some $0<\theta<1$...

If the polynomial $P(x)=a_{0}+a_{1} x+a_{2} x(x-1)+a_{3} x(x-1)(x-2)$interpolates the points $(0,2),(1,3),(2,2)$, and $(3,5)$, then the value of $P\left(\frac{5}{2}\right...

Which one of the given figures $P, Q, R$ and $S$ represents the graph of the following function?$$f(x)=|| x+2|-| x-1||$$$\text{P}$$\text{Q}$$\text{R}$$\text{S}$

The value of$\lim _{x \rightarrow 0} \frac{1}{x} \int_{2}^{2+x}\left(t+\sqrt{t^{2}+5}\right) d t$$0$$4$$5$$6$

Let $f:(0, \infty) \rightarrow \mathbb{R}$ be the continuous function such that $f(x)=2+\frac{g(x)}{x}$ for all $x>0$, where $g(x)=\int_{1}^{x} f(t) d t$ for all $x>0$. T...