Question

find the equation of the tangent line y = ln(x) to the graph at x=e

Answer 1

start by finding the slope of the tangent line by finding y' at x = e

Answer 2

the derivative is 1/x

Answer 3

right, and what's its value when x = e?

Answer 4

1/e

Answer 5

1/e

Answer 6

yeah from here you can use the point slope formula.\[y-y_1=m(x-x_1)\] We found m = 1/3 and were given \(x_1\)= e.

Plug in e to the original equation to get \(y_1\)

Answer 7

one moment while i solve for this please...

Answer 8

y-lne=1/3(x-e) ?

Answer 9

sorry I made a typo. 1/3 is supposed to be 1/e.
and you can simplify \(\ln e\) to 1

Answer 10

oh right! so: y-1=1/e(x-e)

Answer 11

why is the slope 1/e

Answer 12

because the derivative is the slope of the tangent line. Taking the derivative then plugging in e gave the slope

Answer 13

ah! i get it! thank you so much