If [ cdot ] denotes the greatest integer func | vedclass

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(D) We are given the limit $\lim _{x \rightarrow \frac{\pi^{+}}{2}} \frac{[\sin x]-[\cos x]+1}{2}$.As $x \rightarrow \frac{\pi^{+}}{2}$,$x$ is slightl

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$1$

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(D) We are given the limit $\lim _{x \rightarrow \frac{\pi^{+}}{2}} \frac{[\sin x]-[\cos x]+1}{2}$.As $x \rightarrow \frac{\pi^{+}}{2}$,$x$ is slightly greater than $\frac{\pi}{2}$.For $x$ in the interval $(\frac{\pi}{2}, \pi)$,we have $0 \leq \sin x Also,for $x$ in the interval $(\frac{\pi}{2}, \pi)$,we have $-1 Substituting these values into the expression:$\lim _{x \rightarrow \frac{\pi^{+}}{2}} \frac{0 - (-1) + 1}{2} = \frac{1 + 1}{2} = \frac{2}{2} = 1$.

If $[ \cdot ]$ denotes the greatest integer function,then evaluate the limit: $\lim _{x \rightarrow \frac{\pi^{+}}{2}} \frac{[\sin x]-[\cos x]+1}{2}$

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