<p>If there's a function, f(x), and the lim as x approaches 0 is positive infinity (lim x---->0-=+infinity; lim x------>0+=+infinity), then is the limit infinity, or is the answer, "it doesn't exist"?</p>
<p>My book says that a limit at infinity doesn't exist, but I dunno.</p>
<p>If the limit turns out to be infinity or negative infinity, I always write “DNE.”</p>
<p>The limit exists at zero. I can cite a Stewart calculus book for this answer.</p>
<p>For the purposes of the AP Calculus BC exam, would the limit exist? Barron’s AP Cal tells me no.</p>
<p>Infinity is not considered a number, so there is no limit if it approaches zero.</p>
<p>One way to think about it is that the function will grow without a limit to how much it can grow. It extends forever.</p>
<p>Yeah, you’re right, it doesn’t exist, sorry. According to this textbook, for the example 1/x^2 it can be correctly notated as lim x->0 1/x^2 = infinity, but after further research, it still doesn’t exist, sorry about that.</p>
<p>It does not. My AB teacher made this very clear.</p>
<p>Really? Because I learned in calculus that if both one sided limits are the same (even if they are infinity or negative infinity) then the answer is the same as the two sided limits. </p>
<p>I would definitely ask your teacher, though. And if you are still unsure just go with what the book says.</p>
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<p>If a function is approaching positive infinity from both sides, it’s true in a sense that “the limit is infinity,” but infinity isn’t a number.
We say the limit doesn’t exist because the function isn’t approaching any specific numerical value. It doesn’t have to do with one-sided limits.</p>
<p>Halcyonheather, since you took the BC exam, when there was a problem with the limit approaching infinity, what did you answer? DNE?</p>
<p>With multiple-choice, yes. I remember my books making a really big deal out of how infinity isn’t a number. With free-response I could go into more detail about the function approaching infinity, but the limit still doesn’t exist.
Thankfully, a lot of times you won’t get a question that requires you to make a distinction between infinity and other numbers. They’ll give you “does not exist,” and the other choices will be real numbers.</p>
<p>Also, I’ve fallen a bit behind on my BC prep. I haven’t even started integration yet; do you think I’d have time to finish by May?</p>
<p>How much do you know so far? Are you self-studying or taking a class?</p>
<p>AP Calculus BC is supposed to cover college Calculus I and Calculus II. At a college, each of those would be done in a semester, or around four months. So you should finish the AP Calculus AB material by around mid-January and start on the BC material.</p>
<p>I’ve done differentiation, and some applications of differentiation. I’ve also done some parametric and polar stuff.</p>
<p>I’m self studying with a really good tutor.</p>
<p>ahem, yes, 1 + 1 = 2, the square root of 4761 is 69, hmmm yes yes very good.</p>
<p>1+1=5*sqrt(-pi)/0, yakisoba</p>
<p>Get it right omg</p>
<p>@TRG dammit, I forgot to carry the 3. my mistake.</p>
<p>It’s a common mistake, Yakisoba. Just be sure to get it correct in the future ;)</p>