Is the Limit of 5/(x^2 - 4) as x Approaches 2 from the Right Positive Infinity?

In summary, the conversation discusses finding the limit of 5/(x^2 - 4) as x tends to 2 from the right side. Through a table and observation, it is concluded that the limit is positive infinity. The conversation also includes a comment about looking up the answer being for lazy people.
  • #1
nycmathdad
74
0
Find the limit of 5/(x^2 - 4) as x tends to 2 from the right side.

Approaching 2 from the right means that the values of x must be slightly larger than 2.

I created a table for x and f(x).

x...2.1...2.01...2.001
f(x)...12...124.68...1249.68

I can see that f(x) is getting larger and larger and possibly without bound.

I say the limit is positive infinity.

Yes?
 
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  • #2
Problem 1.5.29.
Odd numbered.
Look up the answer.
 
  • #3
For x close to 2 and positive, the denominator, x^2- 4, is close to 0 and positive while the numerator, 5, is positive. That is enough to say that the limit, as x goes to 2 from the right, is positive infinity.
 
  • #4
jonah said:
Problem 1.5.29.
Odd numbered.
Look up the answer.
Well that's no fun!
 
  • #5
Country Boy said:
Well that's no fun!

Exactly. Looking up the answer is for idiots, for lazy pieces of you know what.
 
  • #6
Beer soaked ramblings follow.
nycmathdad said:
Country Boy said:
Well that's no fun!
Exactly. Looking up the answer is for idiots, for lazy pieces of you know what.
Translation: I like it when someone is on my side for a change as opposed to the usual criticism I get. It emboldens me to call people names.

P.S. I just noticed that nycmathdad just got banned again.
 
Last edited:

FAQ: Is the Limit of 5/(x^2 - 4) as x Approaches 2 from the Right Positive Infinity?

What is a limit of a rational function?

A limit of a rational function is the value that a function approaches as the input (x) approaches a certain value. It represents the behavior of the function near that specific input value.

How do you find the limit of a rational function?

To find the limit of a rational function, you can simply plug in the input value (x) into the function and evaluate the resulting expression. If the resulting expression is undefined, you can use algebraic techniques such as factoring or simplifying to find the limit.

What is the difference between a finite and infinite limit of a rational function?

A finite limit of a rational function means that the function approaches a specific value as the input approaches a certain value. An infinite limit means that the function either approaches positive or negative infinity as the input approaches a certain value.

Can a rational function have more than one limit?

Yes, a rational function can have different limits at different input values. This is known as a discontinuity or a removable singularity.

How can the limit of a rational function be used in real life?

The concept of limit of a rational function is used in various fields of science, such as physics, engineering, and economics. It helps in understanding the behavior of a system or function and predicting its future values. For example, in economics, the limit of a demand function can be used to determine the maximum price that consumers are willing to pay for a product.

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