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

In summary, the notation Limh→0+ (f(rh,h))/h indicates taking the limit of a function f with two variables at a specific point, where the second variable approaches 0 from the positive side. The notation suggests evaluating the function at the point (rh,h) and then taking the limit after dividing the result by h. This notation may be unfamiliar, but it is a simple concept.
  • #1
KUphysstudent
40
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? :)
 
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  • #2
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?
 
  • #3
Math_QED said:
Is f a function of 2 variables?
Yes it is, how did you know? :P
 
  • #4
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.
 
  • #5
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 :)
 

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

1. What is limit notation?

Limit notation is a mathematical representation used to describe the behavior of a function as the input approaches a specific value. It is typically written as "lim x→a f(x)", where "x" is the input variable, "a" is the value the input is approaching, and "f(x)" is the function being evaluated.

2. How is limit notation used?

Limit notation is used to analyze the behavior of a function near a particular point. It helps to determine the exact value or behavior of a function at a given point, even if the function is undefined or has a discontinuity at that point.

3. What is the difference between a one-sided and two-sided limit?

A one-sided limit only considers the behavior of a function as the input approaches a specific value from one direction, either the left or the right. A two-sided limit considers the behavior of a function as the input approaches a specific value from both the left and the right.

4. How is limit notation evaluated?

Limit notation is evaluated by substituting the given value for the input variable and simplifying the resulting expression. If the resulting expression is undefined, further algebraic manipulation or the use of other mathematical tools, such as L'Hôpital's rule, may be necessary.

5. What are some real-world applications of limit notation?

Limit notation is commonly used in physics, engineering, and other scientific fields to model and analyze the behavior of systems. It is also used in economics, finance, and other social sciences to predict the behavior of markets and economies. Additionally, limit notation is used in computer science to analyze the performance of algorithms and programs.

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