Question
Download Solution PDFयदि फलन sgn(ln(sinx)) = 0 है, तो x का मान ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
\(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{{\left| x \right|}}{x},\;\;\;x \ne 0} \\ {0,\;\;\;\;x = 0} \end{array}} \right. = \left\{ {\begin{array}{*{20}{c}} {1,\;\;\;\;\;\;\;if\;\;x > 0} \\ {0,\;\;\;\;\;\;\;if\;\;x = 0\;} \\ { - 1,\;\;\;\;\;\;\;\;\;if\;x < 0} \end{array}} \right.\) द्वारा परिभाषित वास्तविक फलन f: R → R को चिह्न फलन कहा जाता है।
f का डोमेन = f की सीमा = {1, 0, – 1}
चिन्ह फलन के आलेख को नीचे देखा जा सकता है -
गणना:
दिया गया फलन sgn(ln(sinx)) = 0 है।
चूँकि हम जानते हैं कि चिन्ह फलन 0 केवल तब होता है जब x = 0 है।
∴ ln (sinx) = 0
∴ sin (x) = 1
⇒ \({\text{x}} = {2{{n\pi \;}} + {\text{}}\frac{{{\pi }}}{2}}, for \ n \in Z\)Last updated on Jun 18, 2025
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