That's the screwed up thing about these problems... each and every problem on this page is nearly impossible to do.
It takes me like hours for each problem and I don't know wtf the issue is.
For example, the same problem above except with:
(x-1)/(x-2) at the point (3, 2).
So I try to take the derivative...
Code:
1.
(x+h) - 1 x - 1
----------- - ------
(x+h) - 2 x - 2
2.
Since denoms are different, combine 'em.
(x + h - 1) (x - 2) (x - 1) (x + h - 2)
--------------------- - ---------------------
(x + h - 2) (x - 2) (x + h - 2) (x - 2)
(x + h - 1) (x - 2) or
x^2 + hx + 2 - 2x - 2h + 2
minus
(x - 1) (x + h - 2) or
x^2 + hx + 2 - x - h + 2
x^2 + hx + 2 - 2x - 2h + 2
- (x^2 + hx + 2 - x - h + 2)
x^2 cancels out
hx cancels out
both 2s cancel out
leaving..
-2x + x
-2h + h
or.. -x - h
you get:
-x - h 1
---------------------------- * ---
x^2 + hx - 2x - 2h + 8 h
3. h cancels out leaving...
-x - 1
-------------------------
x^2 + 0 - 2x - 0 + 8
or...
-x - 1
----------------
x^2 - 2x + 8
using 3, we get..
-(3) - 1
--------------------
(3)^2 - 2(3) + 8
-4
---
11
y - 2 = - 4/11(x - 3)
y = -4/11x - (12/11) + 22/11
y = -4/11x + 10/11
The book has goddamn y = -x + 5. WTF?
This stuff pisses me off. I spent hours on that first one, hours on this.. and I'm 2 problems through this 30 + problem homework paper due tonight.