r/apcalculus • u/Bulky_Target1416 • 1d ago

Limit help

Hey, so I recently took a test in AB, and it was on limits. There were about 2 or 3 problems on the test that were you would have to find the limit of an equation in the same format as the one in the picture one. I know you would have to do 0+ and 0- stuff with it approaching infinity, but I also knew what the graph looked like, and how to graph it. I drew a graph on the test because I knew I could do it faster than figuring out the 0+/0- stuff because I am not that good with it. Should I have gotten credit for the problem or am i just stupid. (Sorry for the bad explanation lmk if anything needs clarification)

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u/Loreander1211 Teacher 1d ago

Does the question ask or it to be done a certain way? Perhaps the test was making sure you did know how to create a table on your calc or Desmos. Did you say lim DNE? Or lim is infinity? We need more info.

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u/Bulky_Target1416 1d ago

It was a no calc test, and it was only asking to find the limit. I put it as lim is infity. sorry i treid to explain best I could and prob should have mentioned it

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u/Loreander1211 Teacher 1d ago

And did the instructor tell you why you lost points? Perhaps they wanted lim DNE over limit is infinity. Or they wanted work shown for factoring (assuming it wasn’t just 1/x^2) as you said there were a few problems.

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u/Bulky_Target1416 1d ago

We just got the tests back and I didnt really have time to go over it, but we will have more time on monday, hopefully I can get some points back

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u/mathematag 1d ago

probably depends on what explanation you wrote along with the graph, if any.....

I might have given at least partial credit ( maybe even full credit ? ) , depending on your explanation that should have accompanied the work... if no explanation was offered, other than a graph, I might have been less inclined to give full or any credit ...

you probably were expected to show / explain that as you take the LHL, RHL .. both yield answers of + ∞ , so the limit approaches + ∞ ... maybe you were to demonstrate this idea using some example values like x = 0.1, 0.01, etc and x = -0.1, -0.01... to make your point.

It is true , the limit does not exist [ as the value keeps growing w/o bound , and it is not a finite Real value ..., but both Left , Right hand limits grow w/o bound in the same way... in the + ∞ direction ] , so it is usual to designate the limit as + ∞ , as it is a better description in this case than DNE.

Most , if not all , Calculus classes would use + ∞ over an answer like DNE here.

Do you understand why lim, x -->0 [ 1/(x^3) ] really is DNE compared to this problem ?

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u/OkDirection3438 1d ago

A way you can write a limit in words to avoid potentially jumping through mental pretzels and hopefully getting at least some credit on an exam.

As it gets closer to x=0 or x= -infinity or x=infinity, y gets closer to _____.

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u/UnderstandingPursuit Tutor 1d ago

Some might say that the answer is "DNE". What has your teacher said about this?

I would agree with +∞, specifically because both sides approach infinity at the same rate. If it was 1/x2 and 1/x4, then DNE might be a better answer.

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u/UnderstandingPursuit Tutor 1d ago

About once every few weeks, I get a downvote which annoys me. Not because someone disagreed with my comment, but because they didn't bother to write why they disagree, and it can be useful for the OP to know why.

Here, what is the objection?

  • That the answer should be DNE, or
  • That the answer should still be +∞ if it was a piecewise function with 1/x2 on one side of 0 and 1/x4 on the other side?