What is the Instantaneous Rate of Change at X=2 for the Function F(x) = 4/(x-1)?

[wearingthin]

Homework Statement

Find the irc at X=2

F(x) = $$\frac{4}{x-1}$$

Homework Equations

$$\stackrel{lim}{h\rightarrow0}$$$$\frac{F(a+h)-F(a)}{h}$$

The Attempt at a Solution

I end up with $$\frac{4}{h+h^{2}}$$ or some other form of an h on the bottom. Is there something else i can do to it??

 

[wearingthin]

$$\frac{4}{(2+h)-1}$$ - $$\frac{4}{2-1}$$

all over h

is how i set it up originally

 

[wearingthin]

and then

$$\frac{4(1)}{(1+h)1}$$ - $$\frac{4(1+4)}{1(1+h)}$$

still all over h

 

[wearingthin]

which becomes


$$\frac{h}{1+h}$$

all over h

right??

 

[Bohrok]

You made the mistake in your third post; that 4 in the very top right should be an h

and then

$$\frac{4(1)}{(1+h)1}$$ - $$\frac{4(1+4)}{1(1+h)}$$

still all over h

First factor out the four so it's easier to work with$$\frac{\frac{4}{h+1} - \frac{4}{1}*\frac{h + 1}{h + 1}}{h} = \frac{4\left(\frac{1}{h + 1} - \frac{h + 1}{h + 1}\right)}{h}$$
then see if you can cancel that h in the denominator.

 

[wearingthin]

IRC = -4

You're a genius! Thank you


-Matt