Question
Download Solution PDF\(\rm \displaystyle\lim_{x\rightarrow 0} \dfrac{|x|}{x}\) का मान क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
एक सीमा के अस्तित्व के लिए बाएं हाथ की सीमा और दाहिने हाथ की सीमा समान होनी चाहिए।
गणना:
एक सीमा के अस्तित्व के लिए बाएं हाथ की सीमा और दाहिने हाथ की सीमा समान होनी चाहिए।
|x| के दो मूल्य हो सकते हैं
|x | = - x जब x है ऋणात्मक हो
|x| = x जब x धनात्मक हो।
\(\rm \displaystyle\lim_{x\rightarrow 0^-} \dfrac{|x|}{x}\) = \(\rm \displaystyle\lim_{x\rightarrow 0} \dfrac{-x}{x} = -1\)
\(\rm \displaystyle\lim_{x\rightarrow 0^+} \dfrac{|x|}{x}\) = \(\rm \displaystyle\lim_{x\rightarrow 0} \dfrac{x}{x} = 1\)
यहाँ, \(\rm \displaystyle\lim_{x\rightarrow 0^-} \dfrac{|x|}{x} \neq \rm \displaystyle\lim_{x\rightarrow 0^+}\dfrac{|x|}{x}\)
इसलिए, \(\rm \displaystyle\lim_{x\rightarrow 0} \dfrac{|x|}{x}\) मौजूद नहीं है ।
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