Sorry, I have no idea how to solve this limit problem
I got this answer but it's wrongUse a CAS (Computer Algebra System) to evaluate the following limit:
cos(0)-sec(0)^2)/2
Sorry, I have no idea how to solve this limit problem
I got this answer but it's wrongUse a CAS (Computer Algebra System) to evaluate the following limit:
cos(0)-sec(0)^2)/2
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.