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

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Slide68.JPG

  1. Chapter 5 Class 12 Continuity and Differentiability (Term 1)
  2. Serial order wise

Transcript

Question 14 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)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.