Thread: Siplification Needed For Tangent Slope

1. Siplification Needed For Tangent Slope

Find an equation of the tangent line to the curve at the given point:

y=(x-1)/(x-2), (3,2)

And I am using the the formula:

lim as x approaches a = [f(x) - f(a)]/(x-a).

So plugging in what we already know, we get:

[x-1/x-2 - 2]/x-3 = slope of the tangent line

Sooooo I'm wasn't sure how to procede. I tried a few different things and I ended up like this:

So the first thing I did was make the 2 that was being subtracted from the first rational number: [2(x-2)]/(x-2). This would simplify the whole thing to:

[(x-1)-2(x-2)/(x-2)]/x-3. Then I brought the x-3 up:

[(x-1)-2(x-2)]/[(x-2)(x-3)]

I'm stuck.

Any help would be appreciated.

2. Re: Siplification Needed For Tangent Slope

Originally Posted by ubom2
Find an equation of the tangent line to the curve at the given point:

y=(x-1)/(x-2), (3,2)

And I am using the the formula:

lim as x approaches a = [f(x) - f(a)]/(x-a).

So plugging in what we already know, we get:

[x-1/x-2 - 2]/x-3 = slope of the tangent line

Sooooo I'm wasn't sure how to procede. I tried a few different things and I ended up like this:

So the first thing I did was make the 2 that was being subtracted from the first rational number: [2(x-2)]/(x-2). This would simplify the whole thing to:

[(x-1)-2(x-2)/(x-2)]/x-3. Then I brought the x-3 up:

[(x-1)-2(x-2)]/[(x-2)(x-3)] <--- I'll take this line

I'm stuck.

Any help would be appreciated.
All your calculations are OK. Unfortunately you have lost somehow that you are asked to calculate a limit.

You only have to do one step more:

$\displaystyle \lim_{x\to3} \left(\frac{(x-1)-2(x-2)}{(x-2)(x-3)}\right) = \lim_{x\to3} \left( \frac{x-1-2x+4}{(x-2)(x-3)}\right) = \lim_{x\to3} \left( \frac{-x+3}{(x-2)(x-3)} \right)= \lim_{x\to3} \left( \frac{-(x-3)}{(x-2)(x-3)}\right)$

Now cancel!

Determine the limit now.

3. Re: Siplification Needed For Tangent Slope

SOOOOO

the equation for the tangent line would be y = -x + 5!!

Thanks