Lim as X approaches 2 (rationalizing wrong)

  • Thread starter r6mikey
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In summary, the author was having trouble rationalizing the denominator in a homework equation and found that distributing like this solved the problem.
  • #1
r6mikey
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Homework Statement



The limit as x approaches 2 for (X-2)/(sqrt7+x)-(x+1)

Homework Equations





The Attempt at a Solution


I know i have to rationalize the denominator but it seems like I'm doing something very wrong with my distrubution...please help!
 
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  • #2
r6mikey said:

Homework Statement



The limit as x approaches 2 for (X-2)/(sqrt7+x)-(x+1)

The Attempt at a Solution


I know i have to rationalize the denominator but it seems like I'm doing something very wrong with my distrubution...please help!

are X and x supposed to be distinct?

When writing things like this out, it's worth being a bit clearer, since what you've written could be:
[tex]\frac{X-2}{\sqrt{7}+x}-(x+1)[/tex]
or
[tex]\frac{X-2}{(\sqrt{7}+x)-(x+1)}[/tex]

Regardless, I don't see why you would need to rationalize the denominator.
 
  • #3
lim as x approaches 2 for [tex]X-2/\sqrt{7+X}-(x+1)[/tex]

this was the problem..I solved it to be -6/5...I just have a question...i have another similar problem, which also becomes in the indeterminate form.

lim as t approaches 3 for [tex]1-t+\sqrt{1+t}/t-3[/tex]

where do i find more information on how to distribute here? I know i have to rationalize I am just lost in how distribution works with a problem with no parentheses and one with parentheses?

I have 4 different books here, 2 algebra, 2 calculus...and not sure what or where to review this
 
  • #4
In latex the construct for fractions is:
\frac{$numerator}{$denominator}
(You can click on the graphical version to see the code:
[tex]\frac{1}{4}[/tex]
It will make things a bit more legible.

You seem to be using [itex]X[/itex]and [itex]x[/itex] as if they were the same - they're not.

To rationalize:
[tex]\frac{x-2}{\sqrt{7+x}-(x+1)}[/tex]
Multiply by:
[tex]\frac{\sqrt{7+x}+(x+1)}{\sqrt{7+x}+(x+1)}[/tex]

Generally, if you have:
[tex]\sqrt{a} + b[/tex]
you'll want to multiply by
[tex]\sqrt{a} - b [/tex]
since this creates a difference of two squares:
[tex](\sqrt{a} + b)\times(\sqrt{a} - b )=a-b^2[/tex]
 

1. What does "Lim as X approaches 2" mean?

The term "Lim as X approaches 2" is a mathematical notation that represents the limit of a function as the input value (X) approaches a specific number (2). It indicates that we are interested in the behavior of the function as the input value gets closer and closer to 2.

2. What is the purpose of taking the limit as X approaches 2?

The limit as X approaches 2 allows us to analyze the behavior of a function at a specific point, even if the function is undefined at that point. It helps us understand how the function behaves near the point X = 2 and can provide valuable information about the overall behavior of the function.

3. How is the limit as X approaches 2 calculated?

The limit as X approaches 2 can be calculated by plugging in values of X that are very close to 2 into the function and observing the resulting output values. This process is known as "approaching by substitution." Alternatively, we can use algebraic techniques such as factoring or rationalizing the denominator to simplify the function and then plug in X = 2 to find the limit.

4. What does "rationalizing wrong" mean in the context of Lim as X approaches 2?

In mathematics, rationalizing a denominator means eliminating any radical or imaginary numbers from the denominator of a fraction. "Rationalizing wrong" could refer to attempting to rationalize the denominator of a function in an incorrect or ineffective way, which may lead to an incorrect limit value.

5. Can the limit as X approaches 2 be equal to a different value for different functions?

Yes, the limit as X approaches 2 can have different values for different functions. The limit value depends on the behavior of the specific function near the point X = 2 and can vary based on the complexity of the function and the techniques used to calculate it.

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