Visualizing Limits with Factorials and Powers

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In summary, a limit of a function is the value that the function approaches as the input approaches a specific value. To calculate a limit, we plug in values that approach the specific point from both sides and if the function approaches the same value, that is the limit. A one-sided limit only considers values from one side of the point. Limits can be calculated algebraically, but for more complicated functions, graphical or numerical methods may be needed. The common types of limits include constant, infinity, rational, trigonometric, exponential, and logarithmic functions, each requiring different calculation methods.
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sedaw
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how to calculate the limits ?

resize.asp?image=1_124518892.jpg


appreciate any kind of help ...
 
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  • #2


n!/n^n

2^n/n!

n!/2^n

1/n + [1 + (-1)^n] / [2^(1/n)]
 
  • #3


You should show that you have done a little work on the problems.

Here is a hint to visualize some of the limits. n! is the product of n terms, one of them is n and the rest are all less than n. n^n is the product of n terms, all of them are n.
 

1. What is the definition of a limit?

The limit of a function is the value that a function approaches as the input approaches a specific value. In other words, it is the value that a function "approaches", but may not necessarily reach, as the input gets closer and closer to a specific value.

2. How do you calculate the limit of a function?

To calculate the limit of a function at a specific point, we first plug in values that approach the specific point from both sides of the input. If the function approaches the same value from both sides, then that value is the limit. If the function approaches different values from each side, then the limit does not exist.

3. What is a one-sided limit?

A one-sided limit is when we only consider the values of a function from one side of the specific point. This is used when the function is not defined or behaves differently from different sides of the point.

4. Can limits be calculated algebraically?

Yes, limits can be calculated algebraically by using various algebraic techniques such as factoring and simplifying. However, for more complicated functions, we may need to use graphical or numerical methods to find the limit.

5. What are the common types of limits?

The common types of limits include: constant limits, limits at infinity, limits of rational functions, limits of trigonometric functions, and limits of exponential and logarithmic functions. Each type may require different methods for calculation.

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