Question

What is the range of the function f(x) = $\textstyle{\frac{|x-1|}{x-1}}$, x ≠ 1?

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.

Write the value of the determinant : $\begin{vmatrix}102 & 18 & 36 \\ 1 & 3 & 4 \\ 17 & 3 & 6\end{vmatrix}$

If 2 $\left(\begin{array}{l l }3 & 4 \\ 5 & x\end{array}\right)$ + $\left(\begin{array}{l l }1 & y \\ 0 & 5\end{array}\right)$ = $\left(\begin{array}{l l }7 & 0 \\ 10 & 5\end{array}\right)$ find x - y.

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.

If a line has direction ratios 2, – 1, – 2, then what are its direction cosines ?

Find x from the matrix equation $\left(\begin{array}{l l }1 & 3 \\ 4 & 5\end{array}\right)$ $\left(\begin{array}{l }x \\ 2\end{array}\right)$ = $\left(\begin{array}{l }5 \\ 6\end{array}\right)$ .