Mathematics: Post your doubts here!

[daredevil]

I dont get it.. Where did that 1st equation come from? and why are u subtracting the second answer from the first? :/

y=2 is the equation of the straight line
the area under the shaded region = area under line - area under graph

that is why we had to subtract the two integrals

 

[Dug]

I usually get confused when we are asked to find the range of trigonometric functions.. its just too complicated for me! What do I have to consider when solving such questions?

Look at these two functions:
f(x) = 3 - 2sinx for 0 ≤ x < pi
f(x) = 3 - 2sin(1/2x) for 0 ≤ x < pi.

How different would the range of the two functions be?
regards salvatore

qwerty123123 solved it but the range will be different for the second. It's 1 ≤ f(x) < 3 unless you made a typo with the inequality...

 

[salvatore]

The range for those two functions is going to be the exact same, the only thing that is changing is the period.
-2sin(x) means the graph will be flipped and the amplitude will be twice.
3+ means the graph will be translated +3 in the y direction so the range for both is 1=<f(x)<=5

qwerty123123 gave you the correct answer, but if you are still confused as to how to go about it then here goes.
What i do is substitue the whole sinx, sin(1/2x), or for that matter cosx or any other cos or sin function by 1 for the maximun value and -1 for the minimum value. I guess you can check it.
And then it's child's play.
3 - 2(1) = 1 & 3-2(-1) = 5 for both of them.
It's only applies for sin/cos not for tan.

Thanks a lot.. I have one more question.
What if the functions were:
f(x) = 3 - 2sinx for 0 ≤ x < pi
f(x) = 3 - 2sinx for 0 ≤ x < 2pi
Would there be any difference in the ranges? (Notice the domain has changed)..

 

[Rutzaba]

I dont get it.. Where did that 1st equation come from? and why are u subtracting the second answer from the first? :/

wen we square a line and integrate fr given limits it gives us the volume under that p[articular line or curve
wen there is no line given and its a straight line parralel to x axis the eq of line wud be y=2

now see volume under y=2 gives us the complete vol under line ie the whole rectangle
no we dun need the non shaded region of the rectangle
non shaded region of rectangle = vol under the curve

now u kno
vol of shaded + vol of non shaded = vol of total rectangle
so vol of shaded = total (under y=2) - non shaded (under curve)
ask again if u dun get it

 

[PANDA-]

Thanks a lot.. I have one more question.
What if the functions were:
f(x) = 3 - 2sinx for 0 ≤ x < pi
f(x) = 3 - 2sinx for 0 ≤ x < 2pi
Would there be any difference in the ranges? (Notice the domain has changed)..

I see you haven't understood my answer through PM's.
Anyways, the range won't change.

 

[Rutzaba]

guys wch is the toughest p1 ever set? gimme the link...

 

[syed1995]

I see you haven't understood my answer through PM's.
Anyways, the range won't change.

It would change.

there is no sin 270 here.. so no sinx=-1..

so the limits would be 3-2(0) and 3-2(1)
so
3 to 1 would be the limits.. instead of the 5 to 1 in the case of 0<x<2pi.

 

[syed1995]

guys wch is the toughest p1 ever set? gimme the link...

All 2012 papers were the toughest ones I encountered.

 

[Rutzaba]

All 2012 papers were the toughest ones I encountered.

i kno that of experience
p3 vector question was soo confusing may june last q variant 2
un mai se bhi wch one is most?

 

[Magenta]

Hi, I need help with june 2012 p1 variant 2. Question 7. Please, I'd really appreciate it!

 

[Rutzaba]

Hi, I need help with june 2012 p1 variant 2. Question 7. Please, I'd really appreciate it!

link

 

[Magenta]

link

http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_s12_qp_12.pdf
Question 7. Thanks!

 

[danyaljamil]

some one please help with q7 part 2 thanks
http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_w12_qp_13.pdf

 

[Rutzaba]

i

http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s12_qp_12.pdf
Question 7. Thanks!

il tell u wat... we haD THIS the year i sat my cie gimme a few mins

 

[iKhaled]

i
il tell u wat... we haD THIS the year i sat my cie gimme a few mins

yeah i remember this question too. everyone was talking about the first part of this question when we did it last year. it was a tricky part and most difficult question on the paper!

 

[Rutzaba]

i did this right.
but tell me isnt a+ (n-1)(d) for arithematic progression?
and ar for geometric :/ ?

 

[WayneRooney10]

Q2 find f '(x) and see that you will get two terms in x with neg sign hence for all positive values of x it will be a decreasing function
7i
y=5-x
y=11-x^2
sub y you will get 5-x=11-x^2 solve it and take the positive value of x as p and its y coordinate as q

Thanks! And I asked for 7 (ii) not (i), so could you explain that too please?

 

[Magenta]

i did this right.
but tell me isnt a+ (n-1)(d) for arithematic progression?
and ar for geometric :/ ?

Yes, yes. Different formulas for sum though.

 

[Rutzaba]

yeah i remember this question too. everyone was talking about the first part of this question when we did it last year. it was a tricky part and most difficult question on the paper!

do this one... i think my p1s getting rusty...
Dug

 

[Rutzaba]

Yes, yes. Different formulas for sum though.

but the ms is showing opposite :O