Tough Possibly Long Cal I problem need help

**Fyou88** · March 24th 2010, 07:38 PM

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

**pickslides** · March 24th 2010, 07:43 PM

You could try $f(x+h)\approx f(x)+h\times f'(x)$

**Fyou88** · March 24th 2010, 07:45 PM

what is that? limit definition?

**pickslides** · March 24th 2010, 07:53 PM

No its a first order approximation.

It can estimate an answer for you.

**Fyou88** · March 24th 2010, 07:55 PM

can u give an example of a problem using that formula i dunno how to use it?

**Fyou88** · March 24th 2010, 07:58 PM

does this problem have anything to do with Trigonometric Functions or inverse Trigonometric Functions?

**pickslides** · March 24th 2010, 08:24 PM

Originally Posted by Fyou88

can u give an example of a problem using that formula i dunno how to use it?

Estimate $f(0.5)$ where $f(x) = \sin x$

$f(x+h)\approx f(x)+h\times f'(x)$

$f(x) = \sin x \implies f'(x) = \cos x$

$f(x+h)\approx \sin x+h\times \cos x$

Using $f(0.5) = f(0+0.5)$ i.e $x = 0,h=0.5$

$f(0+0.5)\approx \sin 0+0.5 \times \cos 0$

$f(0+0.5)\approx 0+0.5 \times 1 = 0.5$

**Fyou88** · March 25th 2010, 08:01 AM

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??

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