What is the Limit of the Difference Quotient for f(x) = 2/x as h Approaches 0?

[Chas3down]

Homework Statement

(f(x+h) - f(x)) / h

f(x) = 2/x
x = -4

As h approaches 0

Homework Equations

N/A

The Attempt at a Solution

(2/(-4 + h) + 1/2) / h


Don't know where to go from there though, not sure how to simplify.

 

[STEMucator]

Homework Statement

(f(x+h) - f(x)) / h

f(x) = 2/x
x = -4

As h approaches 0

Homework Equations

N/A

The Attempt at a Solution

(2/(-4 + h) + 1/2) / h Don't know where to go from there though, not sure how to simplify.

So you want to compute this :

$lim_{h→0} \frac{f(x+h) - f(x)}{h}$ when $f(x) = \frac{2}{x}$ and $x=-4$.

My advice is leave the x=-4 until the very end in these types of problems and just work with this :

$lim_{h→0} \frac{\frac{2}{x+h} - \frac{2}{x}}{h}$

Find a common denominator for the numerator and simplify it, then apply this rule :

$\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{ad}{bc}$.

You'll be able to find the limit easily afterwards.

 

[tiefenb7]

In response to what Zondrina said...

when simplifying $lim_{h→0} \frac{\frac{2}{x+h} - \frac{2}{x}}{h}$,
I use a method called the butterfly method...

Just cross multiply the denominator of the left fraction with the numerator of the right fraction and the denominator of the right fraction with the numerator with the left fraction and finally multiply the denominators of both fractions to get this...

$\frac{\frac{2x-2(x+h)}{(x+h)x}}{h}$

Then use the rule suggested by Zondrina with the h: $\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{ad}{bc}$

 

[Chas3down]

Got it, thanks a lot guys!