Math help (4 Viewers)

Sy123

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Also I was meaning to post this, but I kept forgetting, but here it is:

Slant Asymptote

You should check out some of his other videos, he is very clear and concise as well (Id post the curve sketching one but it involves calculus in it)
 

HSC2014

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I read somewhere in the year 11 Cambridge textbook that knowledge of oblique asymptotes aren't required until year 12, is this correct? I didn't bother learning it in-depth :|
 

Fawun

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Look at the function again:



The graph cannot be at x=-2 AND x=2.
The point is, at x=2 there is an asymptote, but x=-2 there is no asymptote because it cancels out with the numerator, the only alternative is an open circle.
Oops saw this a little too late but when you draw it, do you draw the line going through the x axis and put the open circle on the 2 on the x axis or?

It is a line going through the centre of gradient
To make graping this straight line easy, just plot (0,0) and the point (We just sub in x=1 to make plotting easier)
Wait so why is 2 square root 2 the y co ordinate again?

Also I was meaning to post this, but I kept forgetting, but here it is:

Slant Asymptote

You should check out some of his other videos, he is very clear and concise as well (Id post the curve sketching one but it involves calculus in it)
Oh wow thank you so much!



Thank the lord that i'm done with graphing. Now it's time for trig :)

I need help with this:



Question J please and thank you :)
 

Sy123

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Oops saw this a little too late but when you draw it, do you draw the line going through the x axis and put the open circle on the 2 on the x axis or?

Like I illustrated after that, you take the limit of the x value where the open circle should be, in this case we take the limit of x=-2 because the open circle is at x=-2. If it was at x= k then we take the limit of x=k of the function. When we get a pair of coordinates in this case (-2, 1/4), we plot the open cirlce as just a small open cirlce white inside black outline where that point is, the graph then goes through this open circle.
Wait so why is 2 square root 2 the y co ordinate again?
It can be any coordinate just if it satisfies the function, if I picked x=2, then y would be 2 root 2 times 2. It just helps us in graping the line more accurately since its an inequality graph.

Oh wow thank you so much!



Thank the lord that i'm done with graphing. Now it's time for trig :)

I need help with this:



Question J please and thank you :)
Ok for j, we have to first of all extend the domain given, at this moment it is



So we now need to find the domain for 3theta not just theta otherwise we will lose solutions So lets times 3 to every part of our domain



Now lets evaluate it:



We have square rooted and hence on the RHS given us a square root.

Now tan of something is equal to one, then something must be 45 degrees right? (Exact ratios)
If you remember the ASTC method of determining whether tan is positive or negative, then you will know that in first quadrant and 3rd quadrant tan is positive, and in the other ones negative, here we have plus AND minus 1, this means that our theta can be in ANY quadrant, so we account for all quadrants because it is plus minus.

So now we follow the ASTC rule and the 180-theta, 180+theta etc. etc. rules



Now divide 3 to everything





And the final solutions are all those values above (all in degree measure, it would be a pain to write \circ for each one)
 

kazemagic

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alright fawun this is for your own good, idc if u ignore it, that's ur loss. Get a private tutor, you lack the basic foundations. Get the basics right first then get a class tutor. If this goes on, you wont learn anything and you will be wasting time and money. BOS wont always be able to explain the concepts, theres always a limit on how well words can teach.
 

Fawun

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So now we follow the ASTC rule and the 180-theta, 180+theta etc. etc. rules



Now divide 3 to everything





And the final solutions are all those values above (all in degree measure, it would be a pain to write \circ for each one)
Wait do I ALWAYS have to find the positives and the negatives for theta?

alright fawun this is for your own good, idc if u ignore it, that's ur loss. Get a private tutor, you lack the basic foundations. Get the basics right first then get a class tutor. If this goes on, you wont learn anything and you will be wasting time and money. BOS wont always be able to explain the concepts, theres always a limit on how well words can teach.
I know... I want a better tutor as well and as a matter of fact, my dad spoke to me about the whole tutoring situation yesterday where he said that he wants me to use my brain and to continue going to the class tutor because he thinks i'm not trying hard just because I don't like the tutor.

*sigh*

all stayshun to central
hi
 

kazemagic

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Wait do I ALWAYS have to find the positives and the negatives for theta?



I know... I want a better tutor as well and as a matter of fact, my dad spoke to me about the whole tutoring situation yesterday where he said that he wants me to use my brain and to continue going to the class tutor because he thinks i'm not trying hard just because I don't like the tutor.

*sigh*



hi
you dont need a better tutor for now. Just get a tutor that will build ur foundations. Tell ur dad that classes wont be able to solve ur problem, since the nature of classes isnt to tackle your problems specifically. Your problem is the lack of foundations. No matter how hard u work, it will all be useless if ur not on the right track.

If your dad thinks ur not dedicated enough, just tell ur dad that ur going to contribute to the new tuition fees with ur money from work.
 

Sy123

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Wait do I ALWAYS have to find the positives and the negatives for theta?
The only reason why I chose to find both the negatives and positives, is because my simplification is BOTH negative AND positive.

When we square root something, we do

And that means we have two paths in a way, a positive path and a negative path, the positive path will lead us to the values of theta for positive 1, and the negative will lead us to the valeus of theta for negative 1.

Then we apply ASTC for their respective 'paths'
 

Fawun

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State whether it has any points at which it is not differentiable



I have no idea what to do...
 

Carrotsticks

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Sketch the curve and look to see if there's anything funky like sharp points, discontinuities etc.
 

RivalryofTroll

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I know that but there are no absolute values in here...



Yeah that's the problem

I don't know how to sketch the curve
It's just piece meal functions (sketch each graph separately for each domain) and I said e.g. sharp corners from Absolute Value graphs so that's an example not saying that it's applicable here.

You could use the methods that's in textbooks but looking at it graphically is much easier.
 

Carrotsticks

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C'mon guys seriously? If they can't graph it, they can't graph it. No need to ridicule them...
 

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