Question

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 $\stackrel{\rightarrow}{a}$.$\stackrel{\rightarrow}{b}$,If $\stackrel{\rightarrow}{a}$ = $-\stackrel{\wedge}{i}+\stackrel{\wedge}{j} -2\stackrel{\wedge}{k}$ and $\stackrel{\rightarrow}{b}$ = $2\stackrel{\wedge}{i}+3\stackrel{\wedge}{j} -\stackrel{\wedge}{k}$.

If A is a 3 × 3 matrix, $|A|\neq0$ and $|3A|\,=\,k|A|,$ then write the value of k.

Evaluate $\textstyle\int\!{\frac{(1+\log x)^{2}}{x}}\,d x\,.$

If A is a matrix of order 3 x 4 and B is a matrix of order 4 x 3, then find order of matrix (AB.)

If $\stackrel{\rightarrow}{a}\$ and $\stackrel{\rightarrow}{b}\$ denote the position vectors of points A and B respectively and C is a point on AB such that AC = 2 CB, then write the position vector of C.

If $\stackrel{\rightarrow}{a}\$ =$4\stackrel{\wedge}{i}-\stackrel{\wedge}{j} +\stackrel{\wedge}{k}$ and $\stackrel{\rightarrow}{b}\$ =$2\stackrel{\wedge}{i}-2\stackrel{\wedge}{j} +\stackrel{\wedge}{k}$ then find a unit vector parallel to the vector $\stackrel{\rightarrow}{a}+\stackrel{\rightarrow}{b}$