Mathematics: Post your doubts here!

[WayneRooney10]

Tried ten to the best of my abilities!! I hope you can do part two now that one is cleared up

Awesome work man! But I do not understand the step where you substitute (cos2x)^2 by 1-sin^2x...Can anyone explain it to me?

 

[LMGD33]

how do u do
http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s12_qp_33.pdf

whole question 10?

I tried i) and stuck when I got w^2= -3 +4i

10i) u-w =4i ----1 and uw = 5--------2
u= 5/w
substitute this in eq 1
5/w -w =4i
5-w^2 = 4i
w^2 +4i -5 =0
w= -4i +/- √{(4i)^2 - 4*-5*1}
w= -41 +/- √(-16+ 20)
w = -4i +2/2 -4i-2/2
w= -2i+1 and -2i-1

u= 5/w
u= 5/1-2i
u= 5(1+2i) /4+1
u= 10i +5/5
u= 2i + 1
and it's conjugate u= 2i-1

ii) Sorry this is a little messy-View attachment 26656
The red shaded region is the answer for part ii

iii) I labeled the length of the real axis that represents the max ReZ
You know that the argument of Z is π/4
Cos π/4 = max ReZ/ √8 + 2
ReZ = 1/√2 * (√8+2)
ReZ= 2+ 2/√2

credit to littlecloud11

 

[LMGD33]

Awesome work man! But I do not understand the step where you substitute (cos2x)^2 by 1-sin^2x...Can anyone explain it to me?

Thanks
It's the first rule of trig, cos^2 + sin^2 = 1 , so cos^2 = 1- sin^2
Hope this helps!

 

[LindaKim123]

LMGD33 isn't part become 5-w^2 =4iw after 5/w-w = 4i?

 

[WayneRooney10]

Thanks
It's the first rule of trig, cos^2 + sin^2 = 1 , so cos^2 = 1- sin^2n
Hope this helps!

But you substituted (cos2x)^2, and not (cosx)^2? Right? Because (Cos2x)^3= (cos2x)^2 x (cos2x).

 

[LMGD33]

LMGD33 isn't part become 5-w^2 =4iw after 5/w-w = 4i?

Yes the OP forgot the w in the first few steps but it has no effect on the final answer, because w here is just like x in a quadratic eqn such as:
ax^2 + bx+c = 0
x = -b +- sqrt ( (b)^2 - 4 (a) (c) ) / 2a
So it doesn't have any effect, thanks for pointing it out!!

 

[LMGD33]

But you substituted (cos2x)^2, and not (cosx)^2? Right? Because (Cos2x)^3= (cos2x)^2 x (cos2x).

You're right, just apply the formula to the question at hand, sorry I wasn't clearer

 

[D0cEngi]

hiii pleaaaase anyone knows from where i can get maths and physics past paper 2013!! theyre gonna be my term exam :S
[email protected]

They will be available on this website after 3 months the May/June session has ended.

 

[LindaKim123]

Yes the OP forgot the w in the first few steps but it has no effect on the final answer, because w here is just like x in a quadratic eqn such as:
ax^2 + bx+c = 0
x = -b +- sqrt ( (b)^2 - 4 (a) (a) ) / 2a
So it doesn't have any effect, thanks for pointing it out!!

Oh!!! Okay! now I got it!! Thanks man! so cool!

 

[LindaKim123]

Another question!!
http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_w11_qp_31.pdf

question 10 b) finding the greatest value of arg z, how should I do it?

 

[SararaIH]

Hey everyone,
I know that there is a saying that you shoudn't work too much or put too much pressure on yourself before the day of your exam. But can anyone give me some tips and advice about what I should do before the day of the exam? Like revision methods or revision styles that should follow? Or what papers I should solve before the day of the exam?

 

[Anika Raisa]

Please HELP!!
Hey can any1 tell me hw to integrate 4x/(4+x^2) ?

Thank u!!
SararaIH
PhyZac .... or any1?

 

[Anika Raisa]

Please HELP!!
Hey can any1 tell me hw to integrate 4x/(4+x^2) ?

Thank u!!
SararaIH
PhyZac .... or any1?

 

[LMGD33]

Hi, just wanted to clear something really simple about the iteration question. When the questions asks to show the result of each iteration to 4 decimal places, how would I present my work?
Like
T1=
T2=
T3=
T4=

And so on?

This is how I like to present it..

 

[LMGD33]

Please HELP!!
Hey can any1 tell me hw to integrate 4x/(4+x^2) ?

Thank u!!
SararaIH
PhyZac .... or any1?

Hello! following the rule where S denotes integration
S f ' (x) / f (x) = ln |f(x) | + c
You realize that 4 + x^2 differentiated is 2x
Now to make the numerator 2x, you simply divide by 2 so 4x/2 = 2x
Now you can integrate to : 1/2 ln (4 + x^2)

 

[SararaIH]

Please HELP!!
Hey can any1 tell me hw to integrate 4x/(4+x^2) ?

Thank u!!
SararaIH
PhyZac .... or any1?

let S be the integration sign
Use this formula: S 1/(x^2+a^2) dx = (1/a)*tan^-1(x/a)

So it will be,

(1/2)*tan^-1(x/2)

I think... :/ I'm not sure though
What's the answer?

 

[Anika Raisa]

Use partial fractions first, then integrate.

hw cn i do partial fraction will i have to break (4+x^2) into two n then....
Thank u!

 

[Anika Raisa]

let S be the integration sign
Use this formula: S 1/(x^2+a^2) dx = (1/a)*tan^-1(x/a)

So it will be,

(1/2)*tan^-1(x/2)

I think... :/ I'm not sure though
What's the answer?

Its part of on 11 31 q 8 ii ....

 

[fathimaash]

Hey ppl. R we provided with the formula sheet for tomorrow's ppr?? Thanks in advance.

 

[Rutzaba]

Please HELP!!
Hey can any1 tell me hw to integrate 4x/(4+x^2) ?

Thank u!!
SararaIH
PhyZac .... or any1?

the rule is that if fx = function
and f' x = its differential
then the integral of f'x/fx = ln fx+c
the differential of 4+x^2 is 2x
so we take 2 common and make the eq
2 integral of 2x/ 4 +x^2
2 ln 4+x^2
hope u got it