फलन f(x) = |x - 3| के संबंध में निम्नलिखित पर विचार कीजिए:

1. f(x), x = 3 पर निरंतर है। 

1. f(x), x = 0 पर अवकलनीय है। 

उपरोक्त कथनों में से कौन-सा/कौन-से कथन सही है/हैं?

  1. केवल 1 
  2. केवल 2 
  3. 1 और 2 दोनों 
  4. ना तो 1 और ना ही 2 

Answer (Detailed Solution Below)

Option 3 : 1 और 2 दोनों 
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Detailed Solution

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संकल्पना:

यदि  है, तो f(x), x = a पर निरंतर है। 

यदि LHD = RHD

 है, तो f(x), x = a पर अवकलनीय है। 

f(x) = |x|, यदि x > 0 है, तो f(x) = x है और यदि x < 0 है, तो f(x) = -x है। 

 

गणना:

LHL = 

RHL = 

f(x = 3) = 0

∴ f(x), x = 3 पर निरंतर है। 

 

LHD = RHD, इसलिए, f(x), x = 0 पर अवकलनीय है। 

अतः विकल्प (3) सही है। 

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