Can Random Methods and Limits Improve My Understanding of Numbers?

[Oh the irony]

Can someone give me a little test problem? An easy one please, I'm new to this lol.
Make the method random, so I have to try all three. Sub,Fac,Conj

 

[LCKurtz]

Can someone give me a little test problem? An easy one please, I'm new to this lol.
Make the method random, so I have to try all three. Sub,Fac,Conj

$$lim_{x\rightarrow 4}\frac {2x-8}{\sqrt x - 2}$$

 

[Oh the irony]

$$lim_{x\rightarrow 4}\frac {2x-8}{\sqrt x - 2}$$

Uhh, I doubt I got it right lol butttt0/2?

If I didn't get it right, can you show me how to do it please? I'm trying to learn calculus by myself... lol I know. I just really want to learn it.

 

[LCKurtz]

No, that isn't right. And even though it's wrong, you would normally simplify 0/2 wouldn't you?

I'll give you a hint. Try rationalizing the denominator.

 

[Oh the irony]

No, that isn't right. And even though it's wrong, you would normally simplify 0/2 wouldn't you?

I'll give you a hint. Try rationalizing the denominator.

lol, Like I said.. Can you show me how to do it.

I seriously just kinda started learning this stuff by myself. I can grasp it, if someone can show me the steps. If I can see the steps, I can understand it. Unless there are certain rules of course that go along with it but those are technically steps.

I don't see how I can rationalize it.

 

[sponsoredwalk]

Haha, that kind of problem haunted me for a long time.

It is specifically because of those problems I appreciate the beauty of the number 1 and the amazing cleverness of it. It also illuminated all that complex multiplication I memorized without a thought to the why

Anyway, www.khanacademy.org has some amazing videos on limits, you should watch them all to get a grasp of what you're doing.

I'll quote something from my book that I think was just a great real life description of limits;

Let us imagine a traveller on a train due in New York at 5:17pm.
He must be there on time, so he continually looks at his watch and checks with the timetable.
He notices:
5.01pm the train is 10 miles out.
5:10pm, the train is 1 mile out.
5:17 exactly the train pulls up at its platform in Grand Central Terminal.

As the distance between the train station and the passenger approaches zero, the time reaches the maximum time allowed: 5:17