Cosine of the acute angle between the curve `y=3^(x-1)log_(e)x` and `y=x^(x)-1`, at the point of intersection `(1,0)` is

Options

A. 0
B. 1
C. `(sqrt3)/(2)`
D. `(1)/(2)`

Answer

B

Explanation

Point of intersection of curves is (1,0).
`y=3^(x-1)ln x`
`therefore" "y'=(3^(x-1))/(x)+3^(x-1)log_(e)3.log_(e)x`
`therefore" "m_(1)=1`
`y=x^(x)-1`
`therefore" "(dy)/(dx)=x^(x)(1+log_(e)x)`
`therefore" "m_(2)=1`
`therefore" Angle between curves is given by"`
`tan theta=|(1-1)/(1+1)|=0" "rArr" "theta=0" "rArr" "cos 0^(@)=1`