Estimate f(0.009) if f(x)=sin(sin(sin(5x)))/cos(sin(x)).
Estimate $\displaystyle f(0.5)$ where $\displaystyle f(x) = \sin x $
$\displaystyle f(x+h)\approx f(x)+h\times f'(x)$
$\displaystyle f(x) = \sin x \implies f'(x) = \cos x$
$\displaystyle f(x+h)\approx \sin x+h\times \cos x$
Using $\displaystyle f(0.5) = f(0+0.5)$ i.e $\displaystyle x = 0,h=0.5$
$\displaystyle f(0+0.5)\approx \sin 0+0.5 \times \cos 0 $
$\displaystyle f(0+0.5)\approx 0+0.5 \times 1 = 0.5$