Limits help!!
So I had to find the limit of the top left expression (attachment to follow) as r tended to infinity.
I completely understand their answer, but I also don't know where I went wrong... basically I don't know if I'm just misunderstanding something fundamental about limits (I'm self taught on this front).
I split the first fraction up by splitting the numerator, and then the second fraction I divided it all by the numerator
aggghhhjjjb
I completely understand their answer, but I also don't know where I went wrong... basically I don't know if I'm just misunderstanding something fundamental about limits (I'm self taught on this front).
I split the first fraction up by splitting the numerator, and then the second fraction I divided it all by the numerator
aggghhhjjjb
Original post by hhattiecc
sorry it's a bit scruffy
Sorry but I cannot follow the attachment.
Please post the actual question in full to see what is going on
Original post by TeeEm
Sorry but I cannot follow the attachment.
Please post the actual question in full to see what is going on
Please post the actual question in full to see what is going on
Sorry, thought that might be an issue.
Basically, it's part of a longer question (which I can no longer access because it was on an online programme and this is the feedback - you annoyingly can't see the question again, but in this case the question as a whole is slightly irrelevant as it's only this bit I'm stuck on) about the ratio test of a series, but the mathsy bit I'm stuck on is finding the limit of the attached expression as r tends to infinity.
The answer I was given is the typed one, and my working out is shown roughly on the right. I only consider the fraction on the left because as it tends to zero, the whole expression should as you're multiplying the fractions rather than adding them.
Original post by hhattiecc
Sorry, thought that might be an issue.
Basically, it's part of a longer question (which I can no longer access because it was on an online programme and this is the feedback - you annoyingly can't see the question again, but in this case the question as a whole is slightly irrelevant as it's only this bit I'm stuck on) about the ratio test of a series, but the mathsy bit I'm stuck on is finding the limit of the attached expression as r tends to infinity.
The answer I was given is the typed one, and my working out is shown roughly on the right. I only consider the fraction on the left because as it tends to zero, the whole expression should as you're multiplying the fractions rather than adding them.
Basically, it's part of a longer question (which I can no longer access because it was on an online programme and this is the feedback - you annoyingly can't see the question again, but in this case the question as a whole is slightly irrelevant as it's only this bit I'm stuck on) about the ratio test of a series, but the mathsy bit I'm stuck on is finding the limit of the attached expression as r tends to infinity.
The answer I was given is the typed one, and my working out is shown roughly on the right. I only consider the fraction on the left because as it tends to zero, the whole expression should as you're multiplying the fractions rather than adding them.
not 100% what you are doing but the limit of each of the two fractions as r tends to infinity is 1
Original post by TeeEm
not 100% what you are doing but the limit of each of the two fractions as r tends to infinity is 1
Well yeah I know, but my question is where did my working go wrong.
Hopefully this makes it clearer what I did?
Original post by hhattiecc
Well yeah I know, but my question is where did my working go wrong.
Hopefully this makes it clearer what I did?
Hopefully this makes it clearer what I did?
I have not got the faintest idea where you are getting the first first line ...
It is not the same as what you posted in the attachment of post 4
Original post by TeeEm
I have not got the faintest idea where you are getting the first first line ...
It is not the same as what you posted in the attachment of post 4
It is not the same as what you posted in the attachment of post 4
Right okay, well the top line is the same expression as the question gives, I've just swapped the denominators around.
Then, the first line of working (i.e the "=....." bit) has just come from splitting up the numerator so I have two seperate fractions instead of one. e.g (x+y)/z = x/z + y/z, just like that. I'm only doing this to the fraction on the left - this working isn't simplifying, or even taking into consideration, the fraction on the right.
It's not the same as what I did before because I've just put more steps inbetween instead of just skipping to the simplification I had before. If you look at my working you see the same line of working as before just further down.
According to my working, the first fraction tends to 0. This is why I don't simplify the fraction on the right (of the top line), because 0 x anything = 0, so the whole expression should tend to 0.
I'm really sorry but I don't know how I can make this any clearer haha, this is going disastrously
Original post by hhattiecc
Right okay, well the top line is the same expression as the question gives, I've just swapped the denominators around.
Then, the first line of working (i.e the "=....." bit) has just come from splitting up the numerator so I have two seperate fractions instead of one. e.g (x+y)/z = x/z + y/z, just like that. I'm only doing this to the fraction on the left - this working isn't simplifying, or even taking into consideration, the fraction on the right.
It's not the same as what I did before because I've just put more steps inbetween instead of just skipping to the simplification I had before. If you look at my working you see the same line of working as before just further down.
According to my working, the first fraction tends to 0. This is why I don't simplify the fraction on the right (of the top line), because 0 x anything = 0, so the whole expression should tend to 0.
I'm really sorry but I don't know how I can make this any clearer haha, this is going disastrously
Then, the first line of working (i.e the "=....." bit) has just come from splitting up the numerator so I have two seperate fractions instead of one. e.g (x+y)/z = x/z + y/z, just like that. I'm only doing this to the fraction on the left - this working isn't simplifying, or even taking into consideration, the fraction on the right.
It's not the same as what I did before because I've just put more steps inbetween instead of just skipping to the simplification I had before. If you look at my working you see the same line of working as before just further down.
According to my working, the first fraction tends to 0. This is why I don't simplify the fraction on the right (of the top line), because 0 x anything = 0, so the whole expression should tend to 0.
I'm really sorry but I don't know how I can make this any clearer haha, this is going disastrously
look
I do not know your level and I am not a purist to advise from an analytical point of view.
"Messing around" with infinities and zeros does not follow the usual logic
(e.g infinity - infinity = can be anything, 0/0 can by anything, 0 x infinity can be anything etc)
However
your expression (as it is) is simple enough and requires very little.
As r tends to infinity you may ignore the 2s
then each of the fractions tend to 1.
it is just 2 lines
(edited 8 years ago)
Original post by hhattiecc
Well yeah I know, but my question is where did my working go wrong.
Hopefully this makes it clearer what I did?
Hopefully this makes it clearer what I did?
You've made things far too difficult for yourself there by trying to rearrange the fractions! The problem is that although you've shown that one thing tends to 0, the second factor that you've labelled 'ignore this for now' CANNOT be ignored! You have r^(1/3) on the top and r^(1/6) on the bottom, so as r gets bigger and bigger your fraction tends to infinity! So you're left with tryng to work out 0 x infinity!
You need to keep similar powers of r in numerator and denominator so they both grow at the same speed and the fractions remain finite when you take the limits.
Quick Reply
Related discussions
- Word count excess
- HND Credit Transfer
- Food tech work count NEA 1
- English Literature A Level NEA
- Getting into med school without alevel chem
- differential equation help
- NEA English Lit
- Parking
- biology help
- A-level Maths, Integration, Finding area between curves & Lines.
- AQA Alevel Englit NEA coursework
- A level psychology 16 markers
- A level options
- Outdoor Balcony Furniture
- First speeding ticket
- Maths Integration
- Why was Herbert Hoover regarded as the worst President?
- AQA English Literature NEA Help!!!
- pet insurance for my cat - URGENT
- Odd personal statement formatting on UCAS site.
Latest
Trending
Last reply 3 days ago
Did Cambridge maths students find maths and further maths a level very easy?Last reply 2 weeks ago
Edexcel A Level Mathematics Paper 2 unofficial mark scheme correct me if wrongMaths
71
Trending
Last reply 3 days ago
Did Cambridge maths students find maths and further maths a level very easy?Last reply 2 weeks ago
Edexcel A Level Mathematics Paper 2 unofficial mark scheme correct me if wrongMaths
71
