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# Limits!!! Watch

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1. I've spent ages trying to work out how to do these but I can't seem to see a way if anyone could point me in the right direction......

Limx->inf (sqrt(x^2 +3x + 1 )) - 1

Limx->0 [(2^x) - 1]/x

I know the answer to the second one is ln2 through subbing in values likes 0.00001 etc. but can't actually get the answer, I keep getting xln2 etc.

thanks
dan
2. (Original post by danhirons)
I've spent ages trying to work out how to do these but I can't seem to see a way if anyone could point me in the right direction......

Limx->inf (sqrt(x^2 +3x + 1 )) - 1

Limx->0 [(2^x) - 1]/x

I know the answer to the second one is ln2 through subbing in values likes 0.00001 etc. but can't actually get the answer, I keep getting xln2 etc.

thanks
dan
for 1)
Take out x as factor from both terms (at the square root x^2)

for 2)
L'Hospital
3. (Original post by ztibor)
for 1)
Take out x as factor from both terms (at the square root x^2)

for 2)
L'Hospital
Thanks, I don't know how/why but I typed question 1 out wrong, instead it should be minus x instead of minus 1 at the end. Should I still approach the question in the same way???
4. Try rationalising first.

5. (Original post by danhirons)
Thanks, I don't know how/why but I typed question 1 out wrong, instead it should be minus x instead of minus 1 at the end. Should I still approach the question in the same way???
No.
Form as Spungo wrote

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Updated: December 12, 2010
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