A rectangle of maximum area is inscribed in an ellipse $$\frac{x^2}{25}+\frac{y^2}{16}=1$$, then its dimensions are

The area bounded between the curve $$x^2=y$$ and the line $$y=4 x$$ is

$$\lim _\limits{x \rightarrow 0} \frac{\cos (m x)-\cos (n x)}{x^2}=$$

The area of the parallelogram whose diagonals are represented by the vectors $$\bar{a}=3 \hat{i}-\hat{j}-2 \hat{k}$$ and $$\bar{b}=-\hat{i}+3 \hat{j}-3 \hat{k}$$ is