## The number of points at which the function f (x) = 1/(x-[x] ) is not continuous is

## (A) 1

## (B) 2

## (C) 3

## (D) none of these

This question is similar to

Ex 5.1, 19 - Chapter 5 Class 12- Continuity and Differentiability

Last updated at Nov. 17, 2021 by Teachoo

This question is similar to

Ex 5.1, 19 - Chapter 5 Class 12- Continuity and Differentiability

Transcript

Question 3 The number of points at which the function f (x) = 1/(π₯β[π₯] ) is not continuous is (A) 1 (B) 2 (C) 3 (D) none of these Given f(x) = 1/(π₯ β [π₯] ) Since Greatest Integer Function changes value on integer numbers Thus, we check continuity When x is not an integer When x is an integer Case 1 : When π is not an integer f(x) = 1/(π₯ β [π₯] ) Let d be any non integer point Now, f(x) is continuous at π₯=π if (π₯π’π¦)β¬(π±βπ ) π(π)=π(π ) (π₯π’π¦)β¬(π±βπ ) π(π) = limβ¬(xβπ) 1/(π₯ β [π₯] ) Putting x = d =1/(π β [π] ) π(π ) =1/(π β [π] ) Since limβ¬(xβπ) π(π₯)= π(π) β΄ π(π₯) is continuous for all non-integer points Case 2 : When x is an integer f(x) = [x] Let c be any integer point Now, f(x) is continuous at π₯ =π if L.H.L = R.H.L = π(π) if (π₯π’π¦)β¬(π±βπ^β ) π(π)=(π₯π’π¦)β¬(π±βπ^+ ) " " π(π)= π(π) LHL at x β c (πππ)β¬(π±βπ^β ) f (x) = (πππ)β¬(π‘βπ) f (c β h) = limβ¬(hβ0) π/((π β β) β [π β π]) = limβ¬(hβ0) π/((π β β) β (π β π)) = limβ¬(hβ0) π/(π β β β π + 1) = limβ¬(hβ0) π/(ββ + 1) = π/(0 + 1) = π/π = 1 RHL at x β c (πππ)β¬(π±βπ^+ ) f (x) = (πππ)β¬(π‘βπ) f (c + h) = limβ¬(hβ0) (π+β)β[π+π] = limβ¬(hβ0) (πββ)β(π) = limβ¬(hβ0) ββ = π Since LHL β RHL β΄ f(x) is not continuous at x = c Hence, f(x) is not continuous at all integral points. β΄ There are infinite number of points where f(x) = 1/(π₯β[π₯] ) is not continuous Since we need to find points where f(x) is not continuous And, our options are (A) 1 (B) 2 (C) 3 (D) none of these So, the correct answer is (D)

NCERT Exemplar - MCQs

Question 1

Question 2 Important

Question 3 You are here

Question 4

Question 5

Question 6 Important

Question 7 Important

Question 8

Question 9 Important

Question 10

Question 11 Important

Question 12

Question 13

Question 14 Important

Question 15

Question 16 Important

Question 17

Question 18 Important

Question 19

Question 20 Important

Question 21

Question 22

Question 23 Important

Question 24

Question 25

Question 26 Important

Chapter 5 Class 12 Continuity and Differentiability (Term 1)

Serial order wise

About the Author

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.