Hi,

I'm not sure how to find out the answer to this qustion so any help would be great. I have a hunch thatKmay be -1 andlmay be +/-4.

Thanks, DLL.

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- May 27th 2009, 09:05 PMDaddy_Long_LegsFinding the Values Using a Limit
Hi,

I'm not sure how to find out the answer to this qustion so any help would be great. I have a hunch that**K**may be -1 and**l**may be +/-4.

Thanks, DLL. - May 27th 2009, 09:14 PMSpec
Try replacing with the Maclaurin series for it.

- May 28th 2009, 02:48 AMDaddy_Long_Legs
Hi,

I tried doing the Maclaurin series but I'm not sure where to go from there. I can't see where finding the values a**k**and**l**comes into it.

Thanks, DLL - May 28th 2009, 03:58 AMHallsofIvy
The denominator is going to 0 so, in order to have any finite limit, the numerator must also go to 0. Since cos(x) goes to 1 as x goes to 0, yes, k must be -1.

You then have . I would suggest using L'Hopital's rule: differentiating numerator and denominator separately, we get where I have multiplied numerator and denominator by l to get "sin(z)/z" as z goes to 0. - May 28th 2009, 07:34 AMSpec
Maclaurin series:

Put that into the limit and you get

We can see that since otherwise the limit wouldn't be finite.

With that out of the way, we have since - May 29th 2009, 04:48 AMDaddy_Long_Legs
HallsofIvy (Wait)

I tried doing the problem the way you sugested but I'm not sure how to find the value of**l**after you get to "sin(z)/z" as z goes to 0. I reasonably certain the value of**l**is -/+4. I just can't seem to find how to find it.

Thanks. - May 29th 2009, 04:55 AMmr fantastic