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reenkam
07-15-2007, 10:03 AM
Okay, so this isn't really for a WIP...though I might use it for one that actually has some math. Really, though, I just have no idea how to do this problem, so if anyone has any idea it'd be great! I'll give rep points as prizes!! :)

..lim.......1/4+1/x
x->-4........4+x

Mac H.
07-15-2007, 10:22 AM
Just pretend that the question is: "Simplify the following formula" instead of "find the limit"..

So you could try re-writing (1/4 + 1/x) ... in the form (A+B)/(xxx) , as an example, and see if you can cancel some terms out.

Then, at the last step, substitute x = -4.

Bingo. Done.

Mac

reenkam
07-15-2007, 10:35 AM
WOW

I have no idea what I was doing before...but it worked out completely fine when I looked at it like that. Thank you sooo much Mac H. You're a life saver...

(what's amusing is that this is 1 of 47 problems...all worth a grand total of 10 points aka 1% of my grade...*sigh* math stinks)

limitedtimeauthor
07-15-2007, 11:00 AM
Just pretend that the question is: "Simplify the following formula" instead of "find the limit"..

So you could try re-writing (1/4 + 1/x) ... in the form (A+B)/(xxx) , as an example, and see if you can cancel some terms out.

Then, at the last step, substitute x = -4.

Bingo. Done.

Mac
Oh, golly... everything is suddenly so clear ...

Like why I didn't take calculus. Please, someone - I need Excedrin! Ouch! Brain huuurrrts.

:D

ltd.

kristie911
07-15-2007, 11:46 AM
I took calculus in high school.

I got a 12% for the first semester...basically all I managed to get right on the quizzes was my name. So, it's lucky for you Mac H. knows his calc...because I definitely would have gotten it wrong. ;)

benbradley
07-15-2007, 05:20 PM
Just pretend that the question is: "Simplify the following formula" instead of "find the limit"..

So you could try re-writing (1/4 + 1/x) ... in the form (A+B)/(xxx) , as an example, and see if you can cancel some terms out.

Then, at the last step, substitute x = -4.

Bingo. Done.

Mac
With a direct substitution of -4 you're dividing by zero in the original equation, which is a no-no.

Someone (probably Newton or Leibnitz) invented something called infinitesimals to get around the problem. I used to know better ways of doing this, but there's this brute-force approach. Evaluate the function for x = -3, then x=-3.9, then x=-3.99. It appears it doesn't "approach" a certain value, but it get larger and larger. Thus one might say (with a math professor looking over you to make sure you understand the ramifications of what you're saying) "the limit is infinity."

And here's an interesting twist, approach it from the other direction, x=-5, x=-4.1, and x=-4.01. The answers are all negative, and become "larger" and "larger" NEGATIVE numbers, going the OPPOSITE direction from the other case. Going in this direction, one might say (with the same caveat) "the limit is negative infinity."

Divisoion by zero is strongly frowned upon, because doing it allows you to prove such politically (and mathematically) incorrect statements such as 1=2.

reenkam
07-15-2007, 06:34 PM
That's exactly what I was doing...and on any test I definitely would have said that the limit didn't exist. But the back of the book told me the answer was -1/16. That didn't work out until I multipled the fractions on top by...4/x I think it was. I don't even know if that's allowed, per se, but it then got the answer -1/16...Hopefully this doesn't come up on a test because I definitely would have done exactly what you said with the limit approached from the left/from the right and said it didn't exist. Then I'd be wrong, apparently.

Mac H.
07-16-2007, 01:50 PM
With a direct substitution of -4 you're dividing by zero in the original equation, which is a no-no.

... Evaluate the function for x = -3, then x=-3.9, then x=-3.99. It appears it doesn't "approach" a certain value, but it get larger and larger. Thus one might say (with a math professor looking over you to make sure you understand the ramifications of what you're saying) "the limit is infinity."

And here's an interesting twist, approach it from the other direction, x=-5, x=-4.1, and x=-4.01. The answers are all negative, and become "larger" and "larger" NEGATIVE numbers, going the OPPOSITE direction from the other case. Going in this direction, one might say (with the same caveat) "the limit is negative infinity."No No No! - the answer in the back of the book is right: -1/16

As you said, you can't divide by zero. Hence, by simplifying, Reekham showed that the original formula is equivalent to '1/4x' for all values except for x=-4.

So the question in the maths book is simply:

"You have a graph of 'y = 1/4x'. The only blemish on the graph is that it is missing a dot at x=-4.

Even though you don't know what the value is at that particular x value (since it is missing a dot), what value is 'y' approaching, as you get closer to x=-4 ?"

Put it that way, the answer is obvious.

Mac

benbradley
07-16-2007, 02:59 PM
No No No! - the answer in the back of the book is right: -1/16

As you said, you can't divide by zero. Hence, by simplifying, Reekham showed that the original formula is equivalent to '1/4x' for all values except for x=-4.
That of course doesn't jibe with what I got, but looking over my post again, I see my mistake, I was putting in a positive 4 (or "almost" 4) in the 1/4+1/x part instead of -4. Now it makes sense.[/quote]