Dekoyl's Questions

[kamil9876]

should be set of all times where they intersect where is the set of all non-negative integers btw.

I don't know why they have ommited infinitely many, as clearly so those two times given are not all of them.

edit: I think you mean't why are only two solutions used to find co-ordinates, because what I did up there is fine for finding time but obviously when finding co-ordinates you're not going to sub in infinitely many points in time. Just notice that position repeats every since that is period of both cos and sin. Therefore the co-ordinates at will have the same position, so finding co-ordiantes at t=0 gives all the co-ordinates in this class. In the other class: all have the same co-ordinates(but are different to the first class), therefore finding for gives you all the co-ordinates in this class. Notice that the union of these two classes is the set I defined at the begginning of the post, hence the only two intersections.

[dekoyl]

^Thanks Kamil
[rh] (LOL How do you do that post-break line?)

A question asks "show that
I just did . Will I get full marks (2 marks)?

The answer is this:

[humph]

Yeah there's nothing wrong with doing most of the working as long as they know that you're actually applying some differentiation rule and not just using your calculator or something. If you want to be certain, you should just write "Using the chain rule, we have that..." to avoid any confusion.

[Flaming_Arrow]

^Thanks Kamil
[rh] (LOL How do you do that post-break line?)

A question asks "show that
I just did . Will I get full marks (2 marks)?

The answer is this: (Image removed from quote.)

you probably will get 2 marks since its only 1 mark for method

[dekoyl]

Could anyone tell me how the line with "Now was obtained?
Question: A toy plane maintains a constant altitude. It starts from a height of 40metres. It flies horizontally at 5m/s.
e) Differentiate implicitly the equation to find
Hence evaluate , in radian per second, when x = 10metres, expressing the answer in exact form.

[Flaming_Arrow]

pythagoras theorem

[dekoyl]

Oh.. So a triangle with horizontal length "x" and vertical length "40". Hmm but how did you come up with that FA? It started at an altitude of 40metres ie. it doesn't create an angle with the horizontal?

Ah nevermind. I see now. A diagram is really needed and they didn't include a very nice one but now I see it. Thanks again!

[brenny]

i thought id use your thread to ask a question of my own.
Consider f(x)=cos^3(x-1) and g(x)=x-1 and let p=sin(1)
a) It asked integral from 0 to 2 of f(x) in terms of p I found that to be 2(p-p^3/3)

but then it asks for the exact value of integral from 0 to 2 of f(x).g(x)  sorry i dont know how to do all the maths symbols on the computer??

[dekoyl]

Q: The graph of a rational function has one straight line asymptote and the other asymptote that is not a straight line .

. Doesn't act as an asymptote here? Or is this just the illusion of x = 0 as an asymptote?

. Again, doesn't the truncus and y = x line act as an asymptote?

(none of the above  is the correct answer)
Thanks!

[GerrySly]

The two asymptotes are and because as then and clearly you can't have

[dekoyl]

Hmm well the answer is and the asymptotes are

[d0minicz]

The truncus doesnt act as an asymptote does it ?

for the above when you divide it you get
so x=0 and are asymptotes , straight and non-straight respectively

[dekoyl]

Ah right I think I got it now! Yeah I don't think the truncus acts as an asymptote.
Thanks!

[Flaming_Arrow]

Ah right I think I got it now! Yeah I don't think the truncus acts as an asymptote.
Thanks!

ye it doesn't

[TrueTears]

To find the asymptotes all you need to do is apply some limits.

let .

Thus the equation will converge to since will become very small.

x = 0 is another asymptote because you can not have

Thus the 2 asymptotes are and