• Support PF! Buy your school textbooks, materials and every day products Here!

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

  • Thread starter Chas3down
  • Start date
  • #1
60
0

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.
 

Answers and Replies

  • #2
Zondrina
Homework Helper
2,065
136

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.
 
  • #3
2
0
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}##
 
Last edited:
  • #4
60
0
Got it, thanks a lot guys!
 

Related Threads for: Limit (f(x+h) - f(x)) / h

  • Last Post
Replies
6
Views
1K
Replies
3
Views
2K
  • Last Post
Replies
6
Views
8K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
5
Views
6K
  • Last Post
Replies
5
Views
17K
Top