# Limits using trig functions

• Sep 26th 2008, 04:59 AM
Cyberman86
Limits 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 AM
mr fantastic
Quote:

Originally Posted by Cyberman86
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

You're expected to recognise the limit as the derivative of sin x (calculated from first principles).
• Sep 26th 2008, 08:49 AM
Showcase_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:

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

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

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

$\displaystyle =cosx$