Tangent lines

[calculusstudent12]

For this problem, how would you find the tangent line?

Line L is tangent to y=ln(x) at point P and passes through the point (0,0). Region R is bounded by the graphs of y=ln(x), line L, and the x-axis. What is the equation of line L.

 

[galactus]

We have \(\displaystyle y=ln(x)\) and a point the line passes through, \(\displaystyle x_{1}=0, \;\ y_{1}=0\).

\(\displaystyle y'=m=\frac{1}{x}\)

Use \(\displaystyle y-y_{1}=m(x-x_{1})\)

Sub in and solve for x. This will give the x coordinate of where the line is tangent to ln(x).

Then, you can easily finish finding the line equation.