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.
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