How Do You Solve a Calculus Limit Involving Negative Infinity?

In summary, if you are trying to solve a problem involving negative infinity, you should try multiplying by the conjugate, and if that doesn't work, you can try dividing by 2X+1.
  • #1
darklordavion
9
0

Homework Statement



Limit: The square root of X^2-3X over 2X+1 as X is going towards negative infinity.



Homework Equations



The square root of X^2-3X over 2X+1 as X is going towards negative infinity.

The Attempt at a Solution



I tried to solve it but I have no idea what to do with the negative infinity part. I mean, if it was one number, I would just sub in that number and maybe factor, I am totally lost!
 
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  • #2
darklordavion said:

Homework Statement



Limit: The square root of X^2-3X over 2X+1 as X is going towards negative infinity.



Homework Equations



The square root of X^2-3X over 2X+1 as X is going towards negative infinity.

The Attempt at a Solution



I tried to solve it but I have no idea what to do with the negative infinity part. I mean, if it was one number, I would just sub in that number and maybe factor, I am totally lost!

[tex]\sqrt{x^2 - 3x} = |x|\sqrt{1 - 3/x}[/tex]
Does that help?
 
  • #3
This: √X^2-3X
lim x→-∞ _________
Divided by 2X+1 Like that ^
 
  • #4
Yes, I understand what the problem is. I was suggesting something that might help you with it.
 
  • #5
WHy can't you use L'Hospital's rule?
 
  • #6
Mark44 said:
Yes, I understand what the problem is. I was suggesting something that might help you with it.

Oh sorry :( lol, I thought you interpreted it wrong.

I've tried just subing a random number, which was 4 and got 2/9... not sure what to do next.
 
  • #7
multiply by the conjugate

it is like multiplying by 1, which is not ilegal, but it will cancel out things to you and make life easier
 
  • #8
stonecoldgen said:
multiply by the conjugate

it is like multiplying by 1, which is not ilegal, but it will cancel out things to you and make life easier

can you show me?
 
  • #9
Never mind, a friend who took BC cal last year helped me through AIM.

I got it :) Less work than needed too :)
 
  • #10
darklordavion said:
can you show me?
We are not here to do your work for you. Several people have suggested things to try. Pick one of the techniques and see what you get.

If you haven't taken a close look at the rules of Physics Forums (which you agreed to abide by when you joined it), you can find them here: https://www.physicsforums.com/showthread.php?t=414380

The section on Homework Help is applicable here.
 

FAQ: How Do You Solve a Calculus Limit Involving Negative Infinity?

What is a limit in calculus?

A limit in calculus is a fundamental concept that represents the behavior of a function as the input approaches a certain value. It is used to describe the values that a function approaches as the input gets closer and closer to a specific value.

Why are limits important in calculus?

Limits are important in calculus because they allow us to understand the behavior of a function near a specific point. They are used to define continuity, derivatives, and integrals, which are crucial concepts in calculus and many other areas of mathematics and science.

How do you evaluate a limit in calculus?

To evaluate a limit in calculus, you can use algebraic techniques, such as factoring and cancelling, or you can use graphical methods, such as finding the left and right-hand limits and determining if they are equal. You can also use the limit laws, which state that the limit of a sum, difference, product, or quotient is equal to the sum, difference, product, or quotient of the individual limits.

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

A one-sided limit is the value that a function approaches from only one direction, either from the left or the right. A two-sided limit, also known as a two-tailed limit, is the value that a function approaches from both the left and the right. The two-sided limit only exists if the one-sided limits from both directions are equal.

How can limits be used in real-life applications?

Limits are used in real-life applications to describe the behavior of physical systems and natural phenomena. For example, in physics, the velocity of an object at a specific time can be found by taking the limit of its average velocity as the time interval approaches zero. In economics, limits are used to model growth and decay in a variety of situations, such as population growth and compound interest.

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