Q. 3 Find smallest positive root of e^-x-cos(x)=0 by fixed point method.  (5marks)

Solution:

To locate the smallest positive root we draw the figures of

y = e^-x and y = cos x

Figure shows that the desired root lies between 0 and π/2 i.e. in (0, π/2).

Now let us try x = cos^-1 (e^-x) = g(x)

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