Question

Is A is square matrix of order 3 and |2A| = k|A|, then find the value of k.

Write the differential equation formed from the equation y = mx + c, where m and c are arbitrary constants.

Evaluate $\textstyle\int$$\frac{x^{3}-1}{x^{2}}d x.$

Find : $\int{\frac{3\,x}{3\,x-1}}\,d x$

Let f : R → R be defined by f(x) = 3x² – 5 and g : R → R be defined by g(x) =${\frac{x}{x^{2}+1}}.$ find gof(x) .

Find the matrix A if $\left(\begin{array}{l l l }9 & -1 & 4 \\ -2 & 1 & 3\end{array}\right)$ = A + $\left(\begin{array}{l l l }1 & 2 & -1 \\ 0 & 4 & 9\end{array}\right)$

The contentment obtained after eating x-units of a new dish at a trial function is given by the function $f(x)=x^{3}+6x^{2}+5x+3.$. If the marginal contentment is defined as the rate of change of f(x) with respect to the number of units consumed at an instant, then find the marginal contentment when three units of dish are consumed.