Solve Simple Limit Problem: (1/x)-(1/2)÷(x-2)

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In summary, the problem asks for the answer to be -.25, but Arildno's second suggestion, writing the expression as a single fraction, is best. The common denominator is 1.
  • #1
swears
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lim x=>2

(1/x) - (1/2)
------------
x-2I was looking through my notes and found this problem. It shows the answer to be -.25, but I don't see how they got that. I know I want to cancel out the (x-2) on both sides of the division bar, but I'm not sure how to do this. Can anyone help me out? Thanks!
 
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  • #2
Have you learned about L'hopital's rule yet?
If you haven't, let your first step be to write your numerator as a single fraction.
 
  • #3
L'Hopital's rule is "overkill" here!

Arildno's second suggestion, writing
[tex]\frac{1}{x}- \frac{1}{2}[/tex]
as a single fraction is best. What is the common denominator?
 
  • #4
arildno said:
Have you learned about L'hopital's rule yet?
If you haven't, let your first step be to write your numerator as a single fraction.

No, never heard of him, sorry.

HallsofIvy said:
L'Hopital's rule is "overkill" here!

Arildno's second suggestion, writing
[tex]\frac{1}{x}- \frac{1}{2}[/tex]
as a single fraction is best. What is the common denominator?

I only see a common numerator of 1 not denominator.

Can I do this:

[tex]\frac{-1}{x-2} [/tex] ?
 
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  • #5
swears said:
No, never heard of him, sorry.



I only see a common numerator of 1 not denominator.

Can I do this:

[tex]\frac{-1}{x-2} [/tex] ?
HORROR OF HORRORS!

NEVER EVER MISTREAT FRACTIONS IN THAT MANNER! :mad: :mad: :mad: :mad:
 
  • #6
umm, OK.

Can someone else help me out?
 
  • #7
Do you even know what a fraction is, or what the symbol x stands for?
 
  • #8
yes, x is a variable. 1/2 is a fraction.
 
  • #9
No. You have completely misunderstood it.
 
  • #10
Riight. Well, are you going to correct me, or just keep criticizing?
 
  • #11
Why don't you sit back and re-think how we add or subtract fractions together?
 
  • #12
I've been looking at this problem for an hour, I obviously don't know how to do it.
 
  • #13
Look at [itex]\frac{1}{x}-\frac{1}{2}[/itex]
How many fractions do you have in this expression?
 
  • #14
arildno said:
Look at [itex]\frac{1}{x}-\frac{1}{2}[/itex]
How many fractions do you have in this expression?

2 fractions
 
  • #15
Correct!
Now, what is a common denominator for those fractions?
 
  • #16
-"this message is too short"- 1?
 
  • #17
i'll give you a hint or two
[tex]\frac{\frac{1}{x} - \frac{1}{2}}{x-2}[/tex]
[tex]=\frac{\frac{2}{2x} - \frac{x}{2x}}{x-2}[/tex]
[tex]=\frac{\frac{2-x}{2x}}{x-2}[/tex]
[tex]=\frac{\frac{-(x-2)}{2x}}{x-2}[/tex]
[tex]=-\frac{1}{2x}[/tex]
then substitue x=2 in there to get your answer of -.25
where i have used the following
[tex]\frac{\frac{a}{b}}{c}=\frac{a}{bc}[/tex]
[tex]2-x=-(x-2)[/tex]
[tex]\frac{a}{b}-\frac{c}{d}=\frac{ad-bc}{bd}[/tex]
[tex]\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}[/tex]
 
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  • #18
Thanks for your help. I'm going to try and soak this in and figure out how u did that.
 
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  • #20
yeah you can do that because for example
[tex]\frac{1\times 2}{2\times 2} = \frac{2}{4}=\frac{1}{2}[/tex]
 
  • #21
Cool, Thanks so much. I totally forgot about that Lowest Common Denominator thing.
 

1. What is a limit problem?

A limit problem is a mathematical concept that deals with the concept of approaching a certain value or point, without actually reaching it. It is often used in calculus to determine the behavior of a function as the input value gets closer and closer to a specific value.

2. How do you solve a simple limit problem?

To solve a simple limit problem, you can use the limit laws, substitution, or algebraic manipulation. The first step is to determine if the limit exists by evaluating the function at the point in question. If the value is undefined, you can try using one of the mentioned methods to evaluate the limit.

3. What is the first step in solving a limit problem?

The first step in solving a limit problem is to determine if the limit exists. This can be done by evaluating the function at the point in question. If the value is undefined, you will need to use one of the methods mentioned to evaluate the limit.

4. How do you use substitution to solve a limit problem?

To use substitution in solving a limit problem, you simply substitute the value of the variable in the limit expression with the value it is approaching. Then, evaluate the function at that point to determine the limit.

5. Can limit problems be solved using algebraic manipulation?

Yes, limit problems can be solved using algebraic manipulation. This involves simplifying the expression algebraically to remove any undefined terms. Then, you can use substitution or the limit laws to evaluate the limit.

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