limit problem with nothing in denominator

[PaulKraemer]

Hi,

I am totally stuck on the following limit problem...

lim as v->3 of v^2(3v- 9)(9-v^3)

....With nothing in the denominator, I don't understand why you can't just use substitution. Substitution would give me an answer of zero, but the back of my book says the answer is not zero.

If anyone can help me out with this, I'd really appreciate it.

Thanks in advance,
Paul

 

[JeffM]

Hi,

I am totally stuck on the following limit problem... I am not sure whether I can help, but first I want to make sure I understand the question.
lim as v->3 of v^2(3v- 9)(9-v^3) Is the function f(v) = v[sup:bu8j4tb7]2[/sup:bu8j4tb7] * (2v - 9) * (9 - v[sup:bu8j4tb7]3[/sup:bu8j4tb7]) or f(v) = v[sup:bu8j4tb7]2(2v - 9)[/sup:bu8j4tb7] * (9 - v[sup:bu8j4tb7]3[/sup:bu8j4tb7]) or f(v) = v[sup:bu8j4tb7][2 * (2v - 9) * (9 - v^3)][/sup:bu8j4tb7]?

....With nothing in the denominator, I don't understand why you can't just use substitution. Substitution would give me an answer of zero, but the back of my book says the answer is not zero.

If anyone can help me out with this, I'd really appreciate it.

Thanks in advance,
Paul

 

[galactus]

Hi,

I am totally stuck on the following limit problem...

lim as v->3 of v^2(3v- 9)(9-v^3)

....With nothing in the denominator, I don't understand why you can't just use substitution. Substitution would give me an answer of zero, but the back of my book says the answer is not zero.

If anyone can help me out with this, I'd really appreciate it.

Thanks in advance,
Paul

\(\displaystyle \lim_{v\to 3} v^{2}(3v-9)(9-v^{3})=0\)

It does indeed have a limit of 0.

 

[PaulKraemer]

Thank you galactus,

<< It does indeed have a limit of 0. >>

So, in limit problems like this where there is nothing in the denominator, is it generally ok just to use substitution? Even if substitution gives you a result of zero?

The answer key in the back of the book I'm reading said the answer is -810. I guess that was just a typo but it through me off.

Thanks again,
Paul

 

[Deleted member 4993]

In limit problems, first thing you should do is to substitute.

If the answer is not "indeterminate" - like 0/0 or inf/inf - the problem is solved!!!