Question

The total expenditure (in ₹) required for providing the cheap edition of a book for poor and deserving students is given by R(x) = 3x² + 36x, where x is the number of set of books. If the marginal expenditure is defined as ${\frac{d R}{d x}},$ write the marginal expenditure required for 1200 such sets.

Find the approximate value of f(3·02), up to 2 places of decimal, where f(x) = 3x² + 5x + 3.

Using properties of determinants, prove that $\begin{vmatrix}x+λ & 2x & 2x \\ 2x & x+λ & 2x \\ 2x & 2x & x+λ\end{vmatrix}$ = $(5x+{\lambda})({\lambda}-x)^{2}.$

Find : $\textstyle\int$${\frac{x^{2}}{x^{4}+x^{2}-2}}d x$

Find the equation(s) of the tangent(s) to the curve y = (x³ – 1) (x – 2) points where the curve intersects the x-axis.

Find the equation of the normal at the point (am², am³) for the curve ay² = x³.

If the radius of sphere is measured as 9 cm with an error of 0.03 cm, then find the approximate error in calculating its surface area.