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Question 12 - NCERT Exemplar - MCQs - Chapter 5 Class 12 Continuity and Differentiability

Last updated at Dec. 16, 2024 by Teachoo

The function f (x) = (4 - x^2)/(4x -x^3 ) is

(A) discontinuous at only one point

(B) discontinuous at exactly two points

(C) discontinuous at exactly three points

(D) none of these

This question is similar to Ex 5.1, 3 (c) - Chapter 5 Class 12 - Continuity and Differentiability

Transcript

Question 12 The function f (x) = (4 โˆ’ ๐‘ฅ^2)/(4๐‘ฅ โˆ’๐‘ฅ^3 ) is (A) discontinuous at only one point (B) discontinuous at exactly two points (C) discontinuous at exactly three points (D) none of these f(x) = (4 โˆ’ ๐‘ฅ^(2 ) )/(4๐‘ฅ โˆ’ ๐‘ฅ^3 ) = (2^2 โˆ’ ๐‘ฅ^(2 ) )/(๐‘ฅ(4 โˆ’ ๐‘ฅ^2)) = ((๐Ÿ โˆ’ ๐’™)(๐Ÿ + ๐’™))/(๐’™(๐Ÿ โˆ’ ๐’™)(๐Ÿ + ๐’™)) If we cancel out (2 โˆ’ ๐‘ฅ) and (2 + ๐‘ฅ) Then, we have to assume that x โ‰  2, and x โ‰  โˆ’2 So, our f(x) becomes f(x) = ๐Ÿ/๐’™ This function is not defined for x = 0 Thus, f(x) is defined for all points except x = 0, 2, โˆ’2 โˆด f(x) is discontinuous at exactly 3 points So, the correct answer is (C)
  1. Chapter 5 Class 12 Continuity and Differentiability
  2. Serial order wise

    3. NCERT Exemplar - MCQs

    Rolle's and Mean Value Theorem →
Rolle's and Mean Value Theorem →
Chapter 5 Class 12 Continuity and Differentiability
Serial order wise

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo