Question

Write fog, if f : R → R and g : R → R are given by f(x) = |x| and g(x) = |5x - 2|.

Write a unit vector in the direction of the sum of vectors ${\vec{a}}{=}2\,\vec{i}+2\,\vec{j}-5\,\vec{k}\ \mathrm{~and}\ \vec{b}=2\,\vec{i}+\vec{j}-{7}\vec{k}.$

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

Write a unit vector in the direction of the sum of vectors : $\stackrel{\rightarrow}{a}\ = 2\stackrel{\wedge}{i}-\stackrel{\wedge}{j} +2\stackrel{\wedge}{k} and \stackrel{\rightarrow}{b}\ = \stackrel{\wedge}{i}+\stackrel{\wedge}{j} +3\stackrel{\wedge}{k}$

What is the degree of the following differential equation ? $5x\biggl(\frac{d y}{d x}\biggr)^{2}-\frac{d^{2}y}{d x^{2}}-6y\;=\log x.$

If a matrix has 5 elements, then write all possible orders it can have.

Find a unit vector parallel to the sum of vectors $\stackrel{\wedge}{i}+\stackrel{\wedge}{j} +\stackrel{\wedge}{k}$ and $2\stackrel{\wedge}{i}-3\stackrel{\wedge}{j} +5\stackrel{\wedge}{k}$