Estimate f(0.009) if f(x)=sin(sin(sin(5x)))/cos(sin(x)). (Wondering)

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- Mar 24th 2010, 07:38 PMFyou88Tough Possibly Long Cal I problem need help
Estimate f(0.009) if f(x)=sin(sin(sin(5x)))/cos(sin(x)). (Wondering)

- Mar 24th 2010, 07:43 PMpickslides
You could try $\displaystyle f(x+h)\approx f(x)+h\times f'(x)$

- Mar 24th 2010, 07:45 PMFyou88
what is that? limit definition?

- Mar 24th 2010, 07:53 PMpickslides
No its a first order approximation.

It can estimate an answer for you. - Mar 24th 2010, 07:55 PMFyou88
can u give an example of a problem using that formula i dunno how to use it?

- Mar 24th 2010, 07:58 PMFyou88
does this problem have anything to do with Trigonometric Functions or inverse Trigonometric Functions?

- Mar 24th 2010, 08:24 PMpickslides
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 $

$\displaystyle f(0+0.5)\approx 0+0.5 \times 1 = 0.5$ - Mar 25th 2010, 08:01 AMFyou88
wow so means i have to find the derivative of sin(sin(sin(5x)))/cos(sin(x))? to get slope? and i would need chain rule??