F(x) = (x+1)/(x-1) a=3
Compute derivative at x = a using the limit definition and find an equation of the tangent line.
I get up to:
[(3+h)+1/(3+h)-1] - 2
____________________
h
but I don't know where to go from there, help!
I'll start at the start. First of all, you should make life as easy for yourself as possible.
So write as .
I'll do it for general a. If you prefer, you can replace all the a's with 3 .......
Note that if f(x) = 1, then since f(x) = 1 for all values of x including x = a + h and x = a.
So you only have to worry about getting for :
Put over a common denominator:
Simplify:
.
So .
Now take the limit
.
When a = 3 the value this limit is equal to .
This means that the gradient of the tangent line is .