Main Limit Theorem: Learn Limits in Words

In summary, the conversation discusses different rules for taking limits of various functions. These rules include: the limit of a constant is the constant itself, the limit of a variable is the limit the variable is taken to, scalars can always be pulled out of the limit, the limit of a sum is the sum of the limits, the limit of a product of multiple functions is the product of limits of each function, etc. These rules are important to understand in order to correctly calculate limits in calculus.
  • #1
hockeyfghts5
15
0
My teacher told me it was best to learn in words. can anyone help me with the correct why to write these.

Let n be positive interger, K be a constant, and f and g be function that have limits at C. then

1. lim k = k
x-> c
2. lim x= c
x-> c
3. lim kf(x) = k lim f(x)
x-> c x-> c
4. lim [ f(x) + g(x)] = lim f(x) + lim g(x)
x-> c x-> c x-> c
5. lim [ f(x) - g(x)] = lim f(x) - lim g(x)
x-> c x-> c x-> c
6. lim [ f(x) * g(x)] = lim f(x) * lim g(x)
x-> c x-> c x-> c
7. lim f(x) = lim f(x) provided that lim g(x) does not equal 0
g(x) x-> c
lim g(x)
x-> c
8.lim [ f(x)]n = [ lim f(x)]n
x-> c x-> c
9.lim n radical f(x)= 2radical f(x), provided lim f(x) is less then 0
x-> c x-> c
when n is even

for example in the book they mention no. 4 as the limit of a sum is the sum of the limits. so can anyone else help me out with the others?
 
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  • #2
1) The limit of a constant is the constant itself.

2) The limit of a variable is the limit the variable is taken to.

3) Scalars can always be pulled out of the limit.

5) The same thing as #4 since subtraction is just the sum of the negative.

6) The limit of the product of multiple functions is the product of limits of each function (aka The limit of the product of two functions is the product of the limits of each of the two functions)

Etc..
 

Related to Main Limit Theorem: Learn Limits in Words

1. What is the Main Limit Theorem?

The Main Limit Theorem is a fundamental concept in calculus that states that the limit of a function at a particular point can be determined by evaluating the behavior of the function at points close to that point. It is used to define and calculate limits, which are essential in many mathematical and scientific applications.

2. Why is the Main Limit Theorem important?

The Main Limit Theorem is important because it allows us to solve complex problems by breaking them down into simpler parts. It is also a crucial tool in understanding the behavior of functions and their limits, which is essential in many scientific fields such as physics, engineering, and economics.

3. How do you apply the Main Limit Theorem?

To apply the Main Limit Theorem, you need to evaluate the behavior of a function at points close to the point of interest. This is done by plugging in values that are closer and closer to the desired point and observing how the function behaves. The limit is then determined by analyzing this behavior and making conclusions based on it.

4. What are some real-life applications of the Main Limit Theorem?

The Main Limit Theorem has many real-life applications, such as predicting stock market trends, designing bridges and buildings, optimizing production processes, and analyzing population growth. It is also used in fields such as medicine, biology, and chemistry to model and understand various natural phenomena.

5. Are there any limitations to the Main Limit Theorem?

While the Main Limit Theorem is a powerful tool, it does have some limitations. It only applies to continuous functions, and there are some cases where it may not accurately predict the behavior of a function at a specific point. Additionally, it is not applicable when dealing with discontinuous functions, such as step functions or functions with holes.

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