Math question 1?

Question

Hi,

Could you please determine the tangent line for the curve y = ln x, in the point (a, ln a)? Also determine a so that this line goes throw Origo. Thank you so much. :)

Answer 1

the slope of the tangent is the derivative at point a
the derivative of ln x is 1/x . at point a the slope is 1/a
so equation of tangent is

y= (1/a)*x +b replacing x by a and y by ln a

ln a = (1/a) *a +b =b+1
so b = lna-1

and the line is y = 1/a +ln a -1