Question

(lim h->0) cos(pi/2+h)-cos(pi/2)/h

Answer 1

\[\lim \rightarrow0 \cos \left( \pi \div2+h\right)-\cos \left( \pi \div2\right) \div h\]

Answer 2

\[\lim_{h \rightarrow 0}\frac{\cos(\frac{\pi}{2}) \cos(h)-\sin(\frac{\pi}{2})\sin(h)-\cos(\frac{\pi}{2})}{h}\]
\[\lim_{h \rightarrow 0}\frac{\cos(\frac{\pi}{2})(\cos(h)-1)-\sin(\frac{\pi}{2})\sin(h)}{h}\]
\[\cos(\frac{\pi}{2}) \lim_{h \rightarrow 0}\frac{\cos(h)-1}{h}-\sin(\frac{\pi}{2})\lim_{h \rightarrow 0}\frac{\sin(h)}{h}\]

Answer 3

\[\cos(\frac{\pi}{2})(0)-\sin(\frac{\pi}{2})(1)=0-\sin(\frac{\pi}{2})(1)=-\sin(\frac{\pi}{2})=-(1)=-1\]