Question

How do I solve (cos(pi/3 +h) - 1/2)/ h as h --> 0 but without lhopitals rule

Answer 1

Okay, 3 things we have to be aware of that will help us get the answer. First we need to know two identities:

\[\lim_{x \rightarrow 0}\frac{ sinx }{ x }=1\]
\[\lim_{x \rightarrow 0}\frac{ cosx - 1 }{ kx }=0\]where k can be any number. So with those two identities being known, use the sum of cosines identity and expand the cos(pi/3 + h) expression, then try to manipulate things so you can use thw 2 identities above.