Question 13 - NCERT Exemplar - MCQs - Chapter 5 Class 12 Continuity and Differentiability (Term 1)
Last updated at Nov. 17, 2021 by Teachoo
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If f (x) = 2x and g (x) = x^2/2+1 , then which of the following can be a discontinuous function
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Question 13
If f (x) = 2x and g (x) = π₯^2/2+1 , then which of the following can be a discontinuous function
(A) π (π₯) + π (π₯) (B) f (x) β g (x)
(C) π (π₯) . π (π₯) (D) π(π₯)/(π(π₯))
Given functions
π(π₯)=2π₯ & π(π₯)=π₯^2/2+1
Checking each option one by one
Option 1
π (π)+ π (π)=2π₯+π₯^2/2+1
=π/π π^π+ππ+π
Continuous since it is a polynomial function
Option 2
π (π)β π (π)=2π₯β(π₯^2/2+1)
=2π₯βπ₯^2/2β1
=βπ/π π^π+ππβπ
Continuous since it is a polynomial function
Option 3
π (π)βπ (π)=2π₯β(π₯^2/2+1)
=(2π₯^3)/2+2π₯
=π^π+ππ
Continuous since it is a polynomial function
Option 4
(π(π))/(π(π))=((π₯^2/2+ 1))/2π₯
=(((π₯^2 + 2)/2))/2π₯
=(π^π+π)/ππ
Not defined when 4π₯=0
i.e., π=π
β΄ (π(π₯))/(π(π₯)) is a discontinuous function when π₯=0
So, the correct answer is (D)
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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.
