Question

Sketch an appropriate graph to show that the equation cos.x = x has two solutions, one in *>0 and the other in *<0.cos x[5 marks] \begin{array}{l} \text { The Maclaurin series for } \cos x \text { is }\\ 1-\frac{x^{2}}{2 !}+\frac{x^{4}}{4 !}+\ldots \end{array} (i)approximate solutions of the equation Use the first two non-zero terms to find the two (ii)What are the corresponding approximations if you take the first three non-zero terms? (ii)Use the Maclaurin series to show that \sum_{n m}^{\infty} \frac{(-1)^{1+1}}{(2 n)}\left(\frac{\pi}{2}\right)^{2 n}=1

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