# Thread: Tough Possibly Long Cal I problem need help

1. ## Tough Possibly Long Cal I problem need help

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

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

3. what is that? limit definition?

4. No its a first order approximation.

It can estimate an answer for you.

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

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

7. Originally Posted by Fyou88
can u give an example of a problem using that formula i dunno how to use it?
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 $\displaystyle x = 0,h=0.5$

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

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

8. 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??