I got stuck on this one, once i saw the sin, i just didn't know what to do. All this is one problem. The Answer according to the book is Cos(x)

f(x) = sin(x)

f(x) = lim sin(x+h) - sin (x) over h

........h->0

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- Sep 26th 2008, 04:59 AMCyberman86Limits using trig functions
I got stuck on this one, once i saw the sin, i just didn't know what to do. All this is one problem. The Answer according to the book is Cos(x)

f(x) = sin(x)

f(x) = lim sin(x+h) - sin (x) over h

........h->0 - Sep 26th 2008, 05:01 AMmr fantastic
- Sep 26th 2008, 08:49 AMShowcase_22
Interesting, let me give this a bash:

$\displaystyle \frac{f(x+h)-f(x)}{h}=\frac{sin(x+h)-sin x}{h}$

$\displaystyle \frac{sin x cos h+sin h cos x-sinx}{h}$

as h---->0:

$\displaystyle sin h\rightarrow h \, and \, cos h\rightarrow 1$

$\displaystyle \frac{sin x+hcos x-sinx}{h}$

$\displaystyle \frac{hcos x}{h}$

$\displaystyle =cosx$