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x9

Guest

Evaluating limits

lim   (3square root x) -2/x-8       (I am a latex nub sorry)
x->8

and another question I had that doesn't involve changing the variable is

x+3/x^3 +27

I know its a simple factoring method that I have to use, but I just drag at factoring...

x9

Guest

Re: Evaluating limits

I solved the second question on my own, but the first question I don't really understand. I know it involves changing the x variable into another variable. I tried using latex for it, but I couldn't get it to work.

x9

Guest

Re: Evaluating limits

lim   ³√x  - 2 ÷ x-8
x->8

I hope this makes my question more clear. Thanks for any response.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Evaluating limits

silly answer:
Try 8.01 and get near 1/12.
x = y^3
x' = 3y^2 = 12, when y is 2.

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JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Evaluating limits

For

you can use L’Hôpital’s rule.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Evaluating limits

For the second question, your function is defined at x=3 and so you can evaluate directly.

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Why did the vector cross the road?
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x9

Guest

Re: Evaluating limits

hospitals rule?

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Evaluating limits

http://en.wikipedia.org/wiki/L'H%C3%B4pital's_rule

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Evaluating limits

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Why did the vector cross the road?
It wanted to be normal.

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Evaluating limits

I get 1/12.

Hmm.. I've never actually used this before. Does anyone know if limits is in the A level maths syllabus? (apart from very briefly mentioning them at the start of differentiation).

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Evaluating limits

1/12 looks right to me.

I didn't learn limits until the first term of Uni, although we skimmed over it in late Further Maths without actually mentioning the word 'limit'.

We learnt about MacLaurin series in further maths, such as that sin x = x - x³/3! + x^5/5! - ...
And then the teacher spent about 10 minutes mentioning that for small values of x, the higher order terms in that series become neglegible and so sin x ≈ x.

Using that, (sin x)/x ≈ 1, for small x. And it turns out that that's the limit of (sin x)/x as x --> 0.
But we never actually got taught it properly.

L'Hopital comes even later. I'm halfway through my second year of Uni now, and that still hasn't been covered.

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Why did the vector cross the road?
It wanted to be normal.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Evaluating limits

But only when f and g are continuous on (a, b), and g(x) is not 0 for a < x < b.  And it's actually when f(x)->0 as x -> a and g(x)->0 as x->a.  This may feel like nitpicking, but it's of vital importance in mathematics to check preconditions.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Evaluating limits

Ahh ok.. I might have a look myself. American high schools seem to focus quite a lot on limits though?

Obviously maths-related.. but what are you studying at uni?

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Evaluating limits

But only when f and g are continuous on (a, b), and g(x) is not 0 for a < x < b.  And it's actually when f(x)->0 as x -> a and g(x)->0 as x->a.  This may feel like nitpicking, but it's of vital importance in mathematics to check preconditions.

Fair enough. As I said, I haven't been taught it yet, so that was just how I remembered it. What's b though, and what's it for?

Ahh ok.. I might have a look myself. American high schools seem to focus quite a lot on limits though?

Obviously maths-related.. but what are you studying at uni?

I noticed that too, although my experience of American education is limited to American TV programmes. It seems like whenever anyone needs help from one of their friends in "math", it's always limits they're stuck on. And then their friend is all "yeah you need to take the square root of pi and then divide that by the sine function" and then they're all "oh yeah thanks!" and then they start passionately kissing or something.

Anyway, to answer your question, I'm just studying "Maths" at Uni. Sorry my degree doesn't have a more descriptive name.

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Why did the vector cross the road?
It wanted to be normal.

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Evaluating limits

I noticed that too, although my experience of American education is limited to American TV programmes. It seems like whenever anyone needs help from one of their friends in "math", it's always limits they're stuck on. And then their friend is all "yeah you need to take the square root of pi and then divide that by the sine function" and then they're all "oh yeah thanks!" and then they start passionately kissing or something.

Haha. That's also where I'm basing my information. I liked your description

Anyway, to answer your question, I'm just studying "Maths" at Uni. Sorry my degree doesn't have a more descriptive name.

Ohh ok - it's just that a lot of the people I've spoken to at uni do quite a bit of maths, even though they dont actuallly 'read' maths.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Evaluating limits

Fair enough. As I said, I haven't been taught it yet, so that was just how I remembered it. What's b though, and what's it for?

L'Hospital's rule uses that f and g are continuous arbitrarly close to the point in question.  So it must be that they are continuous at some open interval with one endpoint being a.  b is just a label for the other end.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."