Question

Help in limits
Find the
Lim. (1-cost)/t^2
X-->0

Answer 1

\[\lim_{t \rightarrow 0}\frac{ 1-\cos t }{ t^2 }=\lim_{t \rightarrow 0}\frac{ 2 \sin ^2\frac{ t }{ 2 } }{ t^2 }\]
\[=2\lim_{t \rightarrow 0}\frac{ \sin ^2\frac{ t }{ 2 } }{ \frac{ t^2 }{ 4 }\times 4 }=\frac{ 2 }{ 4 }\lim_{t \rightarrow 0}\left( \frac{ \sin \frac{ t }{ 2 } }{ \frac{ t }{ 2 } } \right)^2=?\]