Understanding Limits & Sequences: Get Help Now!

In summary, the conversation is discussing the limit of a given function as n approaches infinity. The original questioner is confused about how to determine the limit and thought it was 0, but the answerer clarifies that it actually converges to -1/2. However, another participant in the conversation disagrees and believes it converges to 0 based on the graph. The method used to find the limit is correct, but it is unclear how the answer of -1/2 was obtained.
  • #1
Firepanda
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0
http://img215.imageshack.us/img215/8624/limitscz6.jpg

That's the question and the answer.

I don't get why it converges to -1/2 and how you can tell just by looking. Maybe I'm not understanding well enough but I understand how to find the limit, just I thought the limit to infinity showed that 0 was what it converged to, not -1/2.

Any help? Thanks.
 
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  • #2
It converges to 0. The source you got -1/2 from is mistaken.
 
Last edited:
  • #3
According to what i see if the graph were drawn, as n-->+infinity, the curve approaches a horizontal asymptote which is the n-axis, meaning that it converges to zero. And the method they used is correct but how they got -1/2, I have no idea.
 

1. What are limits and sequences?

Limits and sequences are fundamental concepts in calculus that deal with the behavior of a function or sequence as its input approaches a certain value or infinity. They help us understand how a function or sequence evolves and approaches a particular value or behavior.

2. Why are limits and sequences important?

Limits and sequences are important because they provide a way to analyze the behavior of functions and sequences in various mathematical applications. They also play a crucial role in understanding derivatives, integrals, and infinite series.

3. How do I find the limit of a function?

To find the limit of a function, you can use various methods such as direct substitution, factoring, and algebraic manipulation. You can also use graphical and numerical approaches like using a calculator or creating a table of values to estimate the limit.

4. What is the difference between a limit and a sequence?

A limit is the value that a function or sequence approaches, while a sequence is a set of numbers arranged in a specific order. A limit is a property of a function, while a sequence is a list of numbers that can be derived from a function.

5. What are some applications of limits and sequences?

Limits and sequences have various applications in mathematics, physics, engineering, and other fields. They are used in optimization problems, calculating the area under a curve, predicting population growth, and in analyzing the behavior of electrical circuits, among many others.

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