Help me to solve this question on maths p3

[sparkie]

The question is
The diagram shows the curve y = sin x/x
for 0 < x ≤ 2p, and its minimum point M.
(i) Show that the x-coordinate of M satisfies the equation
x = tan x. [4]
(ii) The iterative formula
xn+1 = tan−1(xn) + p
can be used to determine the x-coordinate of M. Use this formula to determine the x-coordinate
of M correct to 2 decimal places. Give the result of each iteration to 4 decimal places. [3]

I don't understand the 2nd part(ii) on the mark scheme it only says:
Use the iterative formula correctly at least once
in which does not explain how to apply it and so on.
Can you help me to solve it?
Thanks

 

[sakuragirl07]

about 2nd part, you can substitute any value between 0 and 2p into the iterative formula given to find your answer. you can try putting x = p . have you tried? what is the answer?

 

[azagen]

where did you get this paper?
which year?

 

[sparkie]

2010 Summer P32
http://www.xtremepapers.net/CIE/Interna ... _qp_32.pdf
this one
4th question.
By the way P is Pi not a constant value
I also cannot solve that equation on 1st step (x=tanx)

Can someone solve this question step by step with real values?

 

[Xenon]

M is the minimum point, so u need to start by differentiating the eqn with respect to x by using the quotient rule. U should get something like (xcosx-sinx)/x^2.
Since M is a stationary point, dy/dx=0.
therefore, (xcosx-sinx)/x^2 = 0
or, (xcosx-sinx) = 0
or, xcosx = sinx
or, (xcosx)/cosx = sinx/ tanx
or, x = tanx
the eqn of min point is x =tanx, so the x- coordinate satisfies the eqn.

For the second part, did u do any maths of iteration previously? If yes, then u should be able to do this one also. Just select a value within the range (i suggest pi/2). If no, then u should go back to book and learn it first. Try solving questions from past papers as well, u will find these maths frequently in P2 question papers.