Does anyone have anything at all which could help me learn graphs? (1 Viewer)

[bleakarcher]

This is the one topic that is truly pssing me off in the fact that I cant seem the learn anything on my own. Anyways, thanks in advance guys.

 

[bleakarcher]

I am especially confused by the random statements the author of the cambridge 4U book makes e.g. y approaches something as x approaches something. I understand them, but how where did he/she get that from?

 

[AAEldar]

Post up a specific question and I'll try and work through it.

It really is harder to explain over the internet/through text than in person. Having someone there with you indicating what they're doing is much better.

 

[bleakarcher]

In the solution the author says as x->0+, y->a-, dy/dx->-infinity. Where did the author get this statement from? It is crucial and its one of the problems I am having in understanding the topic.

 

[AAEldar]

I hate this stuff... hahaha. I'll try my best though.

The function given is . It's obvious then that and , due to the square root signs.

So, it says basically "as x approaches 0 from the positive side", that is, as the values of x decrease towards 0 (so for example 1, 0.5, 0.1... to give you an indication of where it's coming from). As this happens, y approaches a from the negative side - not to say that the values are negative, but it's coming from that side (0.1, 0.5, 1.... like that). then approaches infinity because of . As x goes to zero the first fraction becomes some huge number, infinity, and everything added to that still makes infinity (basically). So approaches infinity also from the negative side.

Now the exact same thing happens on the second line but instead as y approaches zero.

 

[bleakarcher]

Eldar, how do you know from which side it is doing so? I understand the rest

 

[AAEldar]

Eldar, how do you know from which side it is doing so? I understand the rest

Well lets look at when x approaches 0 from the positive side. So if you look at the number plane, from the positive side means its going from the right to the left. So the values of x are decreasing by going from the positive numbers to 0. So say it is 0, the only value that y can then take in the original equation is a for it to hold true. i.e., y approaches a. From which side though? Well we see that if the x values are decreasing, then the y values must be increasing so it's from the negative side.

Does that make sense?

The reason for doing this is to get an idea of what the values of x and y are doing and how they are moving about, whilst also finding points of interest.

 

[bleakarcher]

yeh, i understand. thanks man, i cleared up a lot of shit.

 

[AAEldar]

yeh, i understand. thanks man, i cleared up a lot of shit.

No worries.

Definitely took me a little while to get my head around some of the types of questions they ask.

 

[bleakarcher]

One more question mate. Do you always consider when x->0+ and when y->0+?

 

[AAEldar]

One more question mate. Do you always consider when x->0+ and when y->0+?

Actually not sure... I'd say it depends on the equation of the curve. On this one you have to do as it approaches from the positive side because it's undefined from the negative.

If it was a hyperbola for example then you'd probably do as it approaches the asymptote? 0 is always a safe bet though hahah. Good to know what's going on around the origin.

 

[bleakarcher]

Right now, I am still unsure though I learnt a lot from what you said. In fact, I'm going to put it in my favourites right now.

 

[AAEldar]

Right now, I am still unsure though I learnt a lot from what you said. In fact, I'm going to put it in my favourites right now.

Just do a heap of questions and see what's going on. The more you're exposed to it the easier it'll become and if you have any questions just post them up here and I or someone else will surely answer them!

 

[bleakarcher]

Also when u found the domain you it was clear, i undertand x=>0 but how is it that 0<=x<=a and similarly for y?

 

[AAEldar]

Also when u found the domain you it was clear, i undertand x=>0 but how is it that 0<=x<=a and similarly for y?

Well let's assume a is a number to make it easier - 4 for instance.

So, . If x is greater than 4, than the equation doesn't hold. If x IS 4, then y is zero and this is shown through the limits we used. Same approach for using a letter - a.

 

[bleakarcher]

dude, I have another question lol. can u help me sketch x^(3/2)+y^(3/2)=1

 

[bleakarcher]

Dude I got it!

 

[bleakarcher]

I love you man, everything is so clear now. Become a teacher alongside whatever you want to become lol.

 

[AAEldar]

Dude I got it!

I'm glad! Hadn't quite started it yet so that's a bonus hahaha.

I love you man, everything is so clear now. Become a teacher alongside whatever you want to become lol.

That is actually my current career aspiration >.<

 

[bleakarcher]

lol, good.