The area bounded by the coordinate axes and normal to the curve `y=log_(e)x` at the point P( 1 , 0), is

Options

A. `2x+y=2`
B. `x-2y=1`
C. `x-y=1`
D. `x+y=1`

Answer

D

Explanation

We have, `y=log_(e)x implies(dy)/(dx)=(1)/(x)`
`therefore` Slope off normal at P(1,0)=`-(1)/((dy//dx)_((1,0)))=(-1)/(1)=-1`
`therefore`Equatio of normal at P(1,0)
`impliesy-0=(-1)(x-1)`
`impliesy=-x+1`
`impliesx+y=1`