HSC 2014 MX2 Marathon (archive) (1 Viewer)

[hit patel]

Re: HSC 2014 4U Marathon

Ah. Nice question. I tried to draw the arcsin curve of sec x but couldnt but still didnt realise that.

Volume question please if possible. otherwise integration still good.

 

[hit patel]

Re: HSC 2014 4U Marathon

-1<=sec(a)<sec(b)<=1?
which is undefined except a=b=0

wait i though it was secx => 1 secx <= -1

 

[Davo_01]

Re: HSC 2014 4U Marathon

Find

 

[dunjaaa]

Re: HSC 2014 4U Marathon

what i meant was -1 <= sec(a) < sec(b) <= 1 (within the domain) which is undefined unless a=b=0 i tried editing but it still doesnt show, some bug in the system

 

[Davo_01]

Re: HSC 2014 4U Marathon

Volume question please if possible. otherwise integration still good.

OKay let me have a quick look around

 

[hit patel]

Re: HSC 2014 4U Marathon

Find

Do we let x+2 = sqrt (3) tan theta? Does that work?

 

[Davo_01]

Re: HSC 2014 4U Marathon

Find the volume produced by rotating the area bounded by the ellipse: about the y-axis, using cylindrical shells.

 

[dunjaaa]

Re: HSC 2014 4U Marathon

Can u explain what I'm doing wrong, I divide by x and bring the x inside the sqrt. By simplifying, you get lim(n->-infinity)[sqrt(1+4/x+7/x^2)+1] and you get 2. Now i go to check with my calculator by subbing in a large value, it tells me its worth -2 zzz

 

[Davo_01]

Re: HSC 2014 4U Marathon

Do we let x+2 = sqrt (3) tan theta? Does that work?

Maybe, I have never tried it, but I have two different methods, one of them being rationalizing the numerator

 

[Davo_01]

Re: HSC 2014 4U Marathon

Can u explain what I'm doing wrong, I divide by x and bring the x inside the sqrt. By simplifying, you get lim(n->-infinity)[sqrt(1+4/x+7/x^2)+1] and you get 2. Now i go to check with my calculator by subbing in a large value, it tells me its worth -2 zzz

This is why i chose the question . What you need to think about is when you bring the x inside the square root bracket, are you still dividing by x?

Like does the x still remain as x?

 

[dunjaaa]

Re: HSC 2014 4U Marathon

dw I got it, typesetting solution

 

[hit patel]

Re: HSC 2014 4U Marathon

Find the volume produced by rotating the area bounded by the ellipse: about the y-axis, using cylindrical shells.

8pi sqrt(3) - (16pi)/3 ?

 

[hit patel]

Re: HSC 2014 4U Marathon

8pi sqrt(3) - (16pi)/3 ?

Please dont tell me I made careless mistakes. It took me some time to do it.

 

[hit patel]

Re: HSC 2014 4U Marathon

dw I got it, typesetting solution

Yes please tell me what you get so I can see if tan method works.

 

[Davo_01]

Re: HSC 2014 4U Marathon

Please dont tell me I made careless mistakes. It took me some time to do it.

hmm my answer was what was ur integral

 

[Davo_01]

Re: HSC 2014 4U Marathon

Yes please tell me what you get so I can see if tan method works.

answer is -2 btw

 

[hit patel]

Re: HSC 2014 4U Marathon

hmm my answer was what was ur integral

Way off for both.
Integral was 8pi integral_2_0 sqrt (4-(x-2)^2). I obtained this by shifting curve and its equation or not!!!! damn i forgot to shift equation.
after shifting it would become 8pi integral _2_0 sqrt (4-(x^2)). That gets me 16 Pi^2 , i think

 

[dunjaaa]

Re: HSC 2014 4U Marathon

So what I should of done:
Multiple top and bottom by sqrt(x^2+4x+7)-x,
You get lim(n->-infinity) 4x+7/(sqrt(x^2+4x+7)-x),
Divide everything by x,
lim(n->-infinity) [4+7/x]/[-sqrt(1+4/x+7/x^2)-1] (for x negative)
=-2

 

[Davo_01]

Re: HSC 2014 4U Marathon

Way off for both.
Integral was 8pi integral_2_0 sqrt (4-(x-2)^2). I obtained this by shifting curve and its equation or not!!!! damn i forgot to shift equation.
after shifting it would become 8pi integral _2_0 sqrt (4-(x^2))

you forgot the x



edit: my bad my answer is

 

[hit patel]

Re: HSC 2014 4U Marathon

So what I should of done:
Multiple top and bottom by sqrt(x^2+4x+7)-x,
You get lim(n->-infinity) 4x+7/(sqrt(x^2+4x+7)-x),
Divide everything by x,
lim(n->-infinity) [4+7/x]/[-sqrt(1+4/x+7/x^2)-1] (for x negative)
=-2

Dunja can you please try my way? using the x+2 = sqrt(3) tan(theta). I am trying but I am not getting -2. I changed the limits. so that it will approach pi/2