I have a Calculus project. I have to find the following limit without using L'Hospital:
Limit as x approaches a (x->a) of (cos(x)-cos(a))/(x-a)
Thanks in advance.
by defintion
here you have
so you can just say it is the derivative of cos(a) and just state that as the limit, namely, -sin(a)
if you would rather calculate it manually, note that an alternate definition for the derivative is as follows
it is easier to find this particular limit in that form
getting your limit in that form is not as hard as you think
let , then becomes
now proceed using the addition formula for cosine to simplify
(note, you will need your special trig limits here)