Question

If f : R → R is defined by f(x) = 3x + 2, then define f [f(x)].

Evaluate $\textstyle\int{\frac{\cos{\sqrt{x}}}{\sqrt{x}}}\,d x\ .$

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

Find a vector $\stackrel{\rightarrow}{a}\$ of magnitude ${\mathfrak{5}}{\sqrt{2}}$ making an angle of $\frac{\pi}{4}$ with x-axis, $\frac{\pi}{2}$ with y-axis and an acute angle θ with z-axis.

Simplify : cosθ $\left(\begin{array}{l l }cosθ & sinθ \\ -sinθ & cosθ\end{array}\right)$ + sinθ $\left(\begin{array}{l l }sinθ & -cosθ \\ cosθ & sinθ\end{array}\right)$

If $\left(\begin{array}{l l }2x+y & 3y \\ 0 & 4\end{array}\right)$ = $\left(\begin{array}{l l }6 & 0 \\ 0 & 4\end{array}\right)$ then find the value of x.

The value of the determinant of a matrix A of order 3 × 3 is 4. Find the value of |5A|.