Question

For what values of m do the line y = mx and the curve y =
$x \div {x}^{2 } + 1$
enclose a region? Find the

area of the region.​

Answer 1

By equating both equation => mx = x/x^2 + 1

mx(x^2 + 1 ) = x

m(x^2 + 1) = 1 ; dividing both LHS & RHS by x

x^2 + 1 = 1/m

x^2 = (1 - m) / m

x = +- sqrt [ (1 - m) / m ]