Question

Lim (cos (x+h)-cosx/h) =
h⇒0

Answer 1

Cos (x+h)-cos x /h ==> [cos x cos h - sin x sin h - cos x]/h
[cos x (cos h - 1) - sin x sin h]/h
= lim [ cos x (cos h - 1)/h] - lim [sin x sin h/h]
= cos(x) lim [(cos h -1)/h] - sin (x) lim [(sin h)/h]
= h=0 --> cos(x){0} - sin(x){1}
= - sin(x)