AP EAMCET · Maths · Limits
\([x]\) denotes the greatest integer less than or equal to \(x\). If \(\{x\}=x-[x]\) and \(\lim _{x \rightarrow 0^{-}} \frac{\sin ^{-1}(x+[x])}{2-\{x\}}=\theta\), then \(\sin \theta+\cos \theta=\)
- A -1
- B 0
- C 1
- D \(\sqrt{2}\)
Answer & Solution
Correct Answer
(A) -1
Step-by-step Solution
Detailed explanation
As \(x \rightarrow 0^{-}\), \([x]=-1\). As \(x \rightarrow 0^{-}\), \(\{x\}=x-[x]=x-(-1)=x+1\). \(\theta = \lim _{x \rightarrow 0^{-}} \frac{\sin ^{-1}(x+(-1))}{2-(x+1)}\) \(\theta = \lim _{x \rightarrow 0^{-}} \frac{\sin ^{-1}(x-1)}{1-x}\)…
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