Undergrad Understanding the Limit Notation: Is f(rh,h) the Same as f(r+h)-f(h)?

  • Thread starter Thread starter KUphysstudent
  • Start date Start date
  • Tags Tags
    Limit Notation
Click For Summary
SUMMARY

The discussion centers on the mathematical limit notation Limh→0+ (f(rh,h))/h and whether f(rh,h) is equivalent to f(r+h)-f(h). Participants confirm that f is indeed a function of two variables, and the limit expression indicates evaluating f at the point (rh,h) before dividing by h. The notation clarifies the relationship between the two expressions, dispelling initial confusion regarding their equivalence.

PREREQUISITES
  • Understanding of limit notation in calculus
  • Familiarity with functions of multiple variables
  • Basic knowledge of mathematical analysis
  • Proficiency in evaluating limits
NEXT STEPS
  • Study the properties of functions of two variables
  • Learn about limit definitions and their applications in calculus
  • Explore examples of evaluating limits involving multiple variables
  • Investigate the relationship between differentiability and limits in multivariable calculus
USEFUL FOR

Students of calculus, mathematicians, and educators seeking clarity on limit notation and functions of multiple variables.

KUphysstudent
Messages
40
Reaction score
1
Limh→0+ (f(rh,h))/h
Is the f(rh,h) part the same as f(r+h)-f(h)? I have never seen this before and googling for a long time didn't help, there are no videos with this notation and it's not in my book so, am I just to assume it is? because it doesn't look like it should be the same.

Anyone know what f(rh,h) means? :)
 
Physics news on Phys.org
KUphysstudent said:
Limh→0+ (f(rh,h))/h
Is the f(rh,h) part the same as f(r+h)-f(h)? I have never seen this before and googling for a long time didn't help, there are no videos with this notation and it's not in my book so, am I just to assume it is? because it doesn't look like it should be the same.

Anyone know what f(rh,h) means? :)

Is f a function of 2 variables?
 
Math_QED said:
Is f a function of 2 variables?
Yes it is, how did you know? :P
 
KUphysstudent said:
Yes it is, how did you know? :P

The notation suggested it.

The limit in your question is simply

##\lim_{h \to 0+} \frac{f(rh,h)}{h}##

This means that you evaluate ##f## in the point ##(rh,h)## and then take the limit after dividing the result by h.
 
Math_QED said:
The notation suggested it.

The limit in your question is simply

##\lim_{h \to 0+} \frac{f(rh,h)}{h}##

This means that you evaluate ##f## in the point ##(rh,h)## and then take the limit after dividing the result by h.

Oh it was this simple. I was afraid to get guess but thanks really helped me :)
 

Thread 'How does this derivative work? And why the speed of light remains?'

Relativistic Momentum, Mass, and Energy Momentum and mass (...), the classic equations for conserving momentum and energy are not adequate for the analysis of high-speed collisions. (...) The momentum of a particle moving with velocity ##v## is given by $$p=\cfrac{mv}{\sqrt{1-(v^2/c^2)}}\qquad{R-10}$$ ENERGY In relativistic mechanics, as in classic mechanics, the net force on a particle is equal to the time rate of change of the momentum of the particle. Considering one-dimensional...
View full post »

Similar threads

High School Why does the Limit Process give an Exact Slope?
  • · Replies 53 ·
2
Replies
53
Views
6K
Graduate Question about proof of Great Picard Theorem
  • · Replies 3 ·
Replies
3
Views
3K
MHB Help With Limit: a=16, f=${x}^{.25}$
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Question about uniform convergence in a proof
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Derivatives of Standard Functions
  • · Replies 17 ·
Replies
17
Views
2K
Undergrad What is the zero point for Potential Energy and how to find it from integral limits?
  • · Replies 6 ·
Replies
6
Views
2K
Finding the limit for this function of two variables
  • · Replies 7 ·
Replies
7
Views
2K
I want to understand how to use the general equation [f(x) - f(x+h)]/h
  • · Replies 6 ·
Replies
6
Views
17K
MHB Understanding Limits of Differentiability
  • · Replies 36 ·
2
Replies
36
Views
6K
Help with difficult (?) integration
  • · Replies 2 ·
Replies
2
Views
1K