Physical and geometrical meaning of limits

In summary, the physical meaning of limits in mathematics is the behavior of a function as the input approaches a certain value. The geometrical meaning of limits is the idea of a point or a value that a function is approaching on a graph. Limits are used in various real-world applications, such as calculating rates of change, optimization problems, and determining the behavior of a system. There are two types of limits in calculus: one-sided limits and two-sided limits. To find the limit of a function, you can either evaluate the function at the given point or use algebraic techniques and check for any discontinuities or infinite behavior.
  • #1
shivakumar06
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what is physical and geometrical meaning of limits?
 
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  • #2
That's a very broad question. And you have given no context at all!

Please read this first: https://www.physicsforums.com/blog.php?b=3588

Do some research on the topic. Read wikipedia. Read your textbook. Think a bit about it. If you have specific questions after that, feel free to repost.
 
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  • #3
Mathematical operations, in general, do not have specific "geometric" or "physical" meanings. They may have meaning in a given "application" to geometry or physics.
 

Related to Physical and geometrical meaning of limits

1. What is the physical meaning of limits in mathematics?

The physical meaning of limits is the behavior of a function as the input approaches a certain value. It describes the value that a function or sequence is "approaching" or getting closer to, but may not necessarily reach. It is a fundamental concept in calculus and is used to analyze the behavior of functions and their graphs.

2. What is the geometrical meaning of limits?

The geometrical meaning of limits is the idea of a point or a value that a function is approaching on a graph. It represents the behavior of a function near a specific point and can be seen as the slope of the tangent line at that point. The limit also determines whether a function is continuous at a given point on its graph.

3. How are limits used in real-world applications?

Limits are used in various real-world applications, such as calculating rates of change, optimization problems, and determining the behavior of a system. For example, limits are used in physics to study the motion of objects, in economics to analyze supply and demand, and in engineering to design structures and machines.

4. What are the two types of limits in calculus?

The two types of limits in calculus are one-sided limits and two-sided limits. One-sided limits only consider the behavior of a function from one side of the point, while two-sided limits consider the behavior from both sides. One-sided limits are denoted by a plus or minus sign, while two-sided limits are denoted by an equal sign.

5. How do you find the limit of a function?

To find the limit of a function, you can either evaluate the function at the given point or use algebraic techniques. Algebraically, you can factor, simplify, or use L'Hospital's Rule to find the limit. Graphically, you can use a table of values or the graph of the function to approximate the limit. It is important to check for any discontinuities or infinite behavior when finding the limit of a function.

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