The two parts of $100$ for which the sum of double of the first part and the square of the second part is minimum,are

Find the maximum and minimum values of the function given by $h(x) = x + 1, x \in (-1, 1)$.

Let $f(x) = \begin{cases} |x|, & 0 < |x| \le 2 \\ 1, & x = 0 \end{cases}$,then at $x = 0$,$f$ has

Of all the closed cylindrical cans (right circular) with a given volume of $100 \text{ cm}^3$,find the dimensions of the can that has the minimum surface area.

If $a_n$ is the greatest term in the sequence $a_n = \frac{n^3}{n^4+147}$,$n = 1, 2, 3, \ldots$,then $n$ is equal to $..........$.

Let $AP$ and $BQ$ be two vertical poles at points $A$ and $B$,respectively. If $AP=16 \, m, BQ=22 \, m$ and $AB=20 \, m,$ then find the distance of a point $R$ on $AB$ from the point $A$ such that $RP^2 + RQ^2$ is minimum. (in $, m$)