yeah its been 2 weeks already. :( i really need to boost up my studying over limits.

I was wondering if you could do this for me and explain. I just don't understand the last part where it says hospital rule. Thanks a lot for such a favor.

I used those two trigo identity: 1+ tan^2(x)= sec^2(x)

                                                        sec(x)= 1/cos(x) so sec^2(x)= 1^2/cos^2(x)= 1/cos^2(x)

lim x->0 tan^2(x)/x = lim x->0 (sec^2(x)-1)/x

lim x->0 [sec^2(x)]/x  - 1/x = lim x->0 [1/cos^2(x)]/x - 1/x = lim x->0 1/xcos^2(x) - 1/x  using the hospital rule you get lim x->0 0/something - 0/1 = 0

K, you are familiar with L'Hopital's rule, yes?

I'd just like to interject w/ a few comments. I can't really help because this stuff is stacked a lil too far away in my mind and I'd cause more problems than anything.

First off, if you're going into math, engineering, etc... get used to being stuck. You're at the point where this is all very new (very much like learning a new language) and so I would say you'll never be as confused as now so don't give up. But you'll definitely find yourself to be much more stuck w/ a lot less resources to help you like a vg forum lol so you should begin practicing to attack obstacles w/ a different mindset than the one elementary and high school teaches you.

Secondly to some of the responses being fed your way. If I remember correctly, you should not be telling dany about l'hopitals rule as that is a long ways from being taught to him. Finally, someone also mentioned the easier way of discussing derivatives. You'll get to that shortly, but for the purpose of what you're currently doing and what you'll be tested on, you will need to stick to the more tedious method of limits. The whole delta x going to zero is the concept of a derivative which if you hopefully have a competent professor, will be very clear to you.

no :(

thats what i need elaboration on

Ah, you're right! I just checked and I hadn't been taught L'Hopital's rule until second semester of my first year.

so theres a more simplier way to solve it without the l'hospital rule?

i Fear your grammar but you Fear my Math!!!!!!

L'hopital is the simpler way. I knew the results of those few limits you had in your op by quickly doing l'hopitals in my head since they're very simple. Doesn't always work though and you need to have the knowledge of how derivatives work. You're only going to learn this once you're in cal 2 and you've learned sums, limits and sequences n series. For now, you'll have to trudge through the trig identities. Might as well get used to them though because by the end of calculus and differential eqns (dunno what your future plans are), you'll know em like the back of your hand.

Again sorry I can't help, alot of this stuff is too scrambled in my head for me to do more good than bad.

Probably digital design or journalism, depends what college I get in to.

L'Hopital is the simplest way, you do a derivative on top and a derivative in the bottom of your fraction, then you evaluate your limit

ex: lim x->0   (x^2 + 4x)/(x +4)

derivative on top = 2x + 4

derivative in the bottom = 1

then you evaluate your limit

lim x->0 (2x + 4)/1 = [2(0)+4]/1 = 4

 my english is not so great I hope you understand a bit better