HELP Can anyone PLEASE give me a hand with this limit? THANKS ;)

In summary, a limit in mathematics refers to the value that a function or sequence approaches as the input or index approaches a certain value. To solve a limit, you can use algebraic, graphical, or numerical methods. The purpose of finding limits is to understand the behavior of a function or sequence and it can help in determining continuity, differentiability, and evaluating indeterminate forms. An example of solving a limit is finding the limit of f(x) = (x^2 - 1)/(x - 1) as x approaches 1, which is 2. Some common mistakes when solving limits include not considering the behavior of the function on both sides of the input value, dividing by zero, and not simplifying the expression fully.
  • #1
CathyC
4
0
1. Use the sandwich theorem to compute the limit as n goes to infinity of the sequence with the following nth elements:

a(n) = [1 + sin(n*pi/3)cos(n*pi/5) ] / [n^0.5]

I would really appreciate some help with this one guys. If you could please go slow with the answer as my trig is pretty shaky. Thanks for all your help! :)

Cathy
 
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  • #2
You don't really have to use a lot of trig. -1<=sin(x)<=1 and the same for cos(x). No matter what x is. Suggest an upper bound for the value of the numerator.
 

1. What is a limit in mathematics?

A limit in mathematics refers to the value that a function or sequence approaches as the input or index approaches a certain value. It is used to describe the behavior of a function or sequence near a specific input or index.

2. How do you solve a limit?

To solve a limit, you can use algebraic methods such as factoring, rationalizing, or simplifying the expression. You can also use graphical methods by plotting the function or sequence and observing its behavior near the input or index value. Additionally, you can use numerical methods, such as using a calculator or a computer program, to approximate the limit.

3. What is the purpose of finding limits?

The purpose of finding limits is to understand the behavior of a function or sequence near a specific input or index value. It can help in determining the continuity and differentiability of a function, as well as in evaluating indeterminate forms.

4. Can you give an example of solving a limit?

Sure, let's find the limit of the function f(x) = (x^2 - 1)/(x - 1) as x approaches 1. Using algebraic methods, we can simplify the expression to f(x) = x + 1. Therefore, the limit is 2, as the function approaches 2 as x gets closer to 1.

5. What are some common mistakes when solving limits?

Some common mistakes when solving limits include forgetting to consider the behavior of the function on both sides of the input value, dividing by zero, and not simplifying the expression fully. It is also important to check for continuity at the input value, as some limits may not exist if the function is not continuous at that point.

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