Integrate: x^{2}/x^{4}+x^{2}+1 dx

Find the distance of the point (2,3,4,) from the plane r.(3i-6j+2k)= -11

show that the function f: R ---->R given by f(x)=x^{3 }+ x is a bijection.

Integrate :

(sinx + cosx)/sin^4x+cos^4x

Show that the lines :

(x-1) /2 = (y-2) /3 = (z-3) /4 and (x-4) /5 = (y-1) 2 = z

intersect. find their point of intersection.

if y= [log(x+root x^{2}+1)]^{2 }show that (1+x^{2}) d^{2}y/dx^{2} +xdy/dx =2

Integrate: x

^{2}/x^{4}+x^{2}+1 dxFind the distance of the point (2,3,4,) from the plane r.(3i-6j+2k)= -11

show that the function f: R ---->R given by f(x)=x

^{3 }+ x is a bijection.K, x = pi/4 is continuous at x = pi/4

Integrate :

(sinx + cosx)/sin^4x+cos^4x

Show that the lines :

(x-1) /2 = (y-2) /3 = (z-3) /4 and (x-4) /5 = (y-1) 2 = z

intersect. find their point of intersection.

if y= [log(x+root x

^{2}+1)]^{2 }show that (1+x^{2}) d^{2}y/dx^{2}+xdy/dx =2Q. 16. Find the value of ${a}_{23}+a{}_{32}$ in the matrix

A = ${\left[{a}_{ij}\right]}_{3x3}where{a}_{ij}=\left\{\begin{array}{l}\left|2i-j\right|ifij\\ -i+2j+3ifij\end{array}\right.$