What is the Method for Determining Infinity Limits in a Rational Function?

In summary, when finding the limit of a function as x approaches negative infinity or positive infinity, you must divide both the numerator and denominator by the highest exponent of x and then evaluate. In this example, the limit does not exist because the highest exponent in the numerator is larger than the denominator. The process involves plugging in a negative value to test for negative or positive infinity and then simplifying the expression.
  • #1
camboguy
36
0
ok I am confused when x->negative infinity or positive infinity.

for example

lim (5x^3+27)/(20x^2 + 10x + 9)
x-> negative infinty

heres what i think, i want to know if i have the right idea or not.

- so since the top exponent is larger then the denominator the lim DNE and so i plugged in a negative value to test if it is negative or positive infinity so i put in -1 just to test, the thing is i only plunged it into the (5x^3)/(20x^2); I am thinking this is what i do, and then i get a negative value so i am assuming it is negative infinity. that is what the answer is so posed to be, but did i do it how its so posed to be done?
 
Physics news on Phys.org
  • #2
Divide top and bottom by x^2 and get rid of stuff that tends to zero.
 

1. What is an infinity limit?

An infinity limit is a mathematical concept used to describe the behavior of a function as its input approaches a certain value, usually infinity. It is used to determine the value that a function approaches as its input becomes infinitely large or small.

2. How is an infinity limit evaluated?

The evaluation of an infinity limit involves taking the limit of the function as the input approaches the specified value. This is typically done by substituting increasingly large or small values for the input and observing the resulting output values. If the output values approach a specific number, that number is the value of the infinity limit.

3. What is the difference between a one-sided and a two-sided infinity limit?

A one-sided infinity limit only considers the behavior of the function as its input approaches the specified value from one direction, either positive infinity or negative infinity. A two-sided infinity limit takes into account the behavior of the function from both directions, approaching the specified value from both positive and negative infinity.

4. Can infinity limits be used to determine the behavior of a function at infinity?

Yes, infinity limits can be used to determine the behavior of a function at infinity. This is done by taking the limit of the function as its input approaches infinity or negative infinity. The resulting value, if it exists, can provide insight into the long-term behavior of the function.

5. What are some real-world applications of infinity limits?

Infinity limits are used in various fields of science and engineering, such as physics, chemistry, and economics, to model and predict the behavior of complex systems. They are also used in computer science and data analysis to analyze and optimize algorithms and processes that involve large or infinite quantities.

Similar threads

Limit Definition of Derivative as n Approaches Infinity
    • Calculus and Beyond Homework Help
Replies
20
Views
1K
Can the limit of a quotient of trig functions approach a specific value?
    • Calculus and Beyond Homework Help
Replies
2
Views
859
Help Taking the Limit as K goes to infinity
    • Calculus and Beyond Homework Help
Replies
14
Views
2K
I have troubles finding the limit of this piecewise function
    • Calculus and Beyond Homework Help
Replies
9
Views
792
Limit of x^α.sin²(x)/(x+1) as x approaches infinity is?
    • Calculus and Beyond Homework Help
Replies
13
Views
2K
Limit of a fraction as n-> infinity in the numerator and denomominator
    • Calculus and Beyond Homework Help
Replies
17
Views
1K
Limit of Taylor Polynomial for Tn(x) as n Approaches Infinity
    • Calculus and Beyond Homework Help
Replies
2
Views
837
Determining the limit for function of x and y
    • Calculus and Beyond Homework Help
Replies
1
Views
843
I A question about limits and infinity
    • Calculus
Replies
7
Views
1K
How to show that these sequences are summable?
    • Calculus and Beyond Homework Help
Replies
1
Views
231

Hot Threads

Recent Insights

Back
Top