Question

find the linear approximation of f(x)=ln(x) at a=e

Answer 1

just find the equation of the tangnet line at (e,ln(e)=1)

Answer 2

First step find the slope of the line :
Do this by finding the derivative of ln(x)
After you find the derivative evaluate it at your x=a value

Answer 3

Second step plug your info into the point-slope form for a line:
y-y1=m(x-x1)
You already know a point on the line. I already mentioned it.
y-1=m(x-e)
y=m(x-e)+1
Now all you need is m.