Joeboyshop
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Hello,

I have a 2 part limits question, where the first part is a show that the limit is 1, and the second uses the answer to part 1. I have done part one, but I just can't manage part 2 without getting +/- infinity, but I can see from the graph that this isn't the case.
I've attached the question, please help.....!!

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Farhan.Hanif93
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(Original post by Joeboyshop)
Hello,

I have a 2 part limits question, where the first part is a show that the limit is 1, and the second uses the answer to part 1. I have done part one, but I just can't manage part 2 without getting +/- infinity, but I can see from the graph that this isn't the case.
I've attached the question, please help.....!!

Name:  IMG_3357.jpg
Views: 65
Size:  494.3 KB
I can't see a particularly neat way of doing this. The 'obvious' thing to try, L'Hopitals rule, isn't likely to make the working much easier in this case. Your best bet may be to simply find the taylor expansion of the numerator and perform the calculation from there.

What have you tried?
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Joeboyshop
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(Original post by Farhan.Hanif93)
I can't see a particularly neat way of doing this. The 'obvious' thing to try, L'Hopitals rule, isn't likely to make the working much easier in this case. Your best bet may be to simply find the taylor expansion of the numerator and perform the calculation from there.

What have you tried?

Ok thanks, I had a feeling it needed the Taylor expansion, this is an exam question which I was trying, but we haven't covered the l'hopital's rule or Taylor yet, so I really just wanted to make sure there wasn't something blindingly obvious I could have tried, as the first part wasn't too hard. Also Wolfram alpha says the limit is -1/18, and that number is also at the beginning of the Taylor expansion, so I guess they must be related!

thanks anyway
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_gcx
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(Original post by Joeboyshop)
Ok thanks, I had a feeling it needed the Taylor expansion, this is an exam question which I was trying, but we haven't covered the l'hopital's rule or Taylor yet, so I really just wanted to make sure there wasn't something blindingly obvious I could have tried, as the first part wasn't too hard. Also Wolfram alpha says the limit is -1/18, and that number is also at the beginning of the Taylor expansion, so I guess they must be related!

thanks anyway
Yup, once you've taken away the first term (1) and divided by x^2, (from the taylor series expansion of the numerator) you'd just substitute x=0 to get the answer.
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