Question 13 - NCERT Exemplar - MCQs - Chapter 5 Class 12 Continuity and Differentiability (Term 1)

Last updated at Nov. 17, 2021 by Teachoo

Hello! Teachoo has made this answer with days (even weeks!) worth of effort and love. If Teachoo has been of any help to you in your Board exam preparation, then please support us by clicking on this link to make a donation

If f (x) = 2x and g (x) = x^2/2+1 , then which of the following can be a discontinuous function

Hello! Teachoo has made this answer with days (even weeks!) worth of effort and love. If Teachoo has been of any help to you in your Board exam preparation, then please support us by clicking on this link to make a donation

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)

Made by

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.