Question

Using the fact that lim h->0
sin(h)/h =1 and
lim h->0 cos(h)-1/h =0
compute the limit
lim h->0 cos(x+h)-cos(x)/ h

Answer 1

again?

Answer 2

lim h->0 cos(x+h)-cos(x)/ h
=lim h->0 cosxcosh-sinxsinh-cos(x)/ h
=lim h->0 cosx(cosh-1)-sinxsinh/ h
=lim h->0( cosx(cosh-1)/h)-lim h->0sinxsinh/ h
=0-sinx=-sinx

Source: http://www.mathskey.com/question2answer/

Answer 3

dang, guess it didn't work yesterday
lets take it step by step
\[\lim_{h\to 0}\frac{\cos(x+h)-\cos(x)}{h}=\lim_{x\to 0}\frac{\cos(x)\cos(h)-\sin(x)\sin(h)-\cos(x)}{h}\]
is a start