If f (x) = x 2 sin 1/x, where x ≠ 0, then the value of the function f at x = 0, so that the function is continuous at x = 0 , is

(A) 0  

(B) – 1

(C) 1 

(D) none of these

This question is similar to Ex 5.1, 24 - Chapter 5 Class 12 - Continuity and Differentiability

Slide82.JPG

Slide83.JPG
Slide84.JPG

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Question 16 If f (x) = x2 sin 1/𝑥, where x ≠ 0, then the value of the function f at x = 0, so that the function is continuous at x = 0, is (A) 0 (B) – 1 (C) 1 (D) none of these Given f (x) = x2 sin 1/𝑥, when x ≠ 0 To find f (0) f(x) is continuous at 𝑥=0 if L.H.L = R.H.L = 𝑓(0) if lim┬(x→0^− ) 𝑓(𝑥)=lim┬(x→0^+ ) " " 𝑓(𝑥)= 𝑓(0) LHL at x → 0 lim┬(x→0^− ) f(x) = lim┬(h→0) f(0 − h) = lim┬(h→0) f(−h) = lim┬(h→0) (−ℎ)^2 𝒔𝒊𝒏⁡〖𝟏/((−𝒉))〗 = lim┬(h→0) ℎ^2 𝒌 = 02 .𝑘 = 0 RHL at x → 0 lim┬(x→0^+ ) f(x) = lim┬(h→0) f(0 + h) = lim┬(h→0) f(h) = lim┬(h→0) ℎ^2 𝒔𝒊𝒏⁡〖𝟏/𝒉〗 = lim┬(h→0) ℎ^2 𝒌 = 02. 𝑘 = 0 Since, L.H.L = R.H.L = 𝑓(0) 0=𝑓(0) ∴ f (0) =𝟎 So, the correct answer is (A)

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.