निम्नलिखित में से कौन सा \(\rm \lim_{x\rightarrow 3}\frac{|x-3|}{x-3}\) के संबंध में सही है?

This question was previously asked in
NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. सीमा का अस्तित्व है और यह 1 के बराबर है
  2. सीमा का अस्तित्व है और यह 0 के बराबर है
  3. सीमा का अस्तित्व है और यह -1 के बराबर है
  4. सीमा का अस्तित्व नहीं है

Answer (Detailed Solution Below)

Option 4 : सीमा का अस्तित्व नहीं है
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Detailed Solution

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व्याख्या:

दिया गया है:

\(\rm \lim_{x\rightarrow 3}\frac{|x-3|}{x-3}\)

LHL = \(\rm \lim_{x\rightarrow 3}\frac{|x-3|}{x-3} = \frac{-(x-3)}{x-3} = -1\)

RHL = \(\rm \lim_{x\rightarrow 3}\frac{|x-3|}{x-3} = \frac{(x-3)}{x-3} =1\)

LHL ≠ RHL; सीमा का अस्तित्व नहीं है

इसलिए विकल्प (d) सही है।

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