Question

What is the value of $\underset{x\to \frac{\pi }{2}}{lim}\left[\cos x\right]$ ?

Answer 1

Let h be a very small positive number.

${lim}_{x\to \frac{\pi }{2}}\left[\cos (\frac{\pi }{2}-h)\right]\Rightarrow \left[\sin h\right]=0{lim}_{x\to \frac{\pi }{2}}\left[\cos \frac{\pi }{2}\right]=0{lim}_{x\to \frac{\pi }{2}}\left[\cos (\frac{\pi }{2}+h)\right]\Rightarrow \left[\cos (\frac{\pi }{2}-(-h\left)\right)\right]\Rightarrow \left[\sin (-h)\right]=-1{lim}_{x\to {\frac{\pi }{2}}^{+}}\ne {lim}_{x\to {\frac{\pi }{2}}^{-}}Notcontinuous.$