BOOBIES .actually a question on limits approaching infinity

Thread starter banfill_89
Start date Nov 14, 2008
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Infinity Limits

In summary, the limit of approaching infinity refers to the value that a function or expression approaches as the input approaches infinity. To evaluate this limit, algebraic techniques and limit laws can be used. There are two types of limits approaching infinity: horizontal and vertical. A limit approaching infinity can only have one value, and understanding them is important in mathematics for determining function behavior and for use in advanced concepts.

Nov 14, 2008

banfill_89

BOOBIES...actually a question on limits approaching infinity...please help

Homework Statement

lim x^2-x^4
x>Infinity

Homework Equations

i made both of them...e^(2lnx)-e^(4lnx)...then get stuck

im allowed to use limit laws, and no l'hospitals rule

The Attempt at a Solution

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Nov 14, 2008

Dick

Science Advisor

Homework Helper

Word to the wise. x^2-x^4=x^4*(1/x^2-1).

Feb 2, 2009

banfill_89

thanks! sorry for the late reply

FAQ: BOOBIES .actually a question on limits approaching infinity

What is the limit of approaching infinity?

The limit of approaching infinity refers to the value that a function or expression approaches as the input approaches infinity. It can also be described as the value that a sequence of numbers gets closer and closer to as the number of terms in the sequence increases.

How do you evaluate limits approaching infinity?

To evaluate a limit approaching infinity, you can use algebraic techniques such as factoring, rationalizing, or simplifying the expression. You can also use the properties of limits, such as the limit laws, to simplify the expression and find the limit.

What are the different types of limits approaching infinity?

There are two types of limits approaching infinity: horizontal and vertical. A horizontal limit approaching infinity occurs when the value of the function approaches a constant value as the input increases without bound. A vertical limit approaching infinity occurs when the value of the function approaches positive or negative infinity as the input increases without bound.

Can a limit approaching infinity have multiple values?

No, a limit approaching infinity can only have one value. This is because the limit is defined as the value that the function approaches, not the value that it actually reaches. If a function has multiple values as the input approaches infinity, then the limit does not exist.

Why is understanding limits approaching infinity important in mathematics?

Limits approaching infinity are essential in mathematics because they allow us to determine the behavior of a function as the input increases without bound. They also help us to understand the end behavior of a function, which can be useful in applications such as finding the maximum or minimum value of a function. Additionally, limits approaching infinity are used in many advanced mathematical concepts, such as derivatives and integrals.