Sorry, I have no idea how to solve this limit problem

I got this answer but it's wrongQuote:

Use a CAS (Computer Algebra System) to evaluate the following limit:

http://img.photobucket.com/albums/v6...25750img12.gif

cos(0)-sec(0)^2)/2

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- Nov 3rd 2006, 09:21 PMkillasnakeLimit question
Sorry, I have no idea how to solve this limit problem

Quote:

Use a CAS (Computer Algebra System) to evaluate the following limit:

http://img.photobucket.com/albums/v6...25750img12.gif

cos(0)-sec(0)^2)/2 - Nov 4th 2006, 12:01 AMSoltras
Well if you use something like Mathematica (software) it should give you 1/24 as the answer.

To solve it analytically, the easiest way is to use L'Hopital's Rule.

Here's what you start with.

If you substitute 0 in for , then you get which is criterion for using L'Hopitale.

Derive the numerator and denominator with respect to .

The limit becomes:

Once again, direct substitution will yield , so L'Hopitale can be applied again, giving the limit:

Again, direct substitution gives . Do L'Hopitale yet again to get the limit:

You may recognize this form as .

(if you didn't recognize the form, applying L'Hopitale one last time would give 1/24 trivially).

Hope that helps. - Nov 4th 2006, 01:47 AMCaptainBlack