Paper 3 May/June 2009 MATHEMATICH (9709/3) A Levels
لطفا برای اطمینان از عملکرد و تجربه بهتر از مرورگرهای مدرن و به روز مانند کروم یا فایرفاکس استفاده کنید.

a) By sketching suitable graphs, show that the equation
$4{x^2} - 1 = \cot x$
has only one root in the interval $0 \lt x \lt \frac{1}{2}\pi $.
b) Verify by calculation that this root lies between 0.6 and 1.
c) Use the iterative formula
${x_{n + 1}} = \frac{1}{2}\sqrt {\left( {1 + \cot {x_n}} \right)} $
to determine the root correct to 2 decimal places. Give the result of each iteration…