Question 16
If f (x) = x2 sin 1/π₯, where x β 0, then the value of the function f at x = 0, so that the function is continuous at x = 0, is
(A) 0 (B) β 1
(C) 1 (D) none of these
Given
f (x) = x2 sin 1/π₯, when x β 0
To find f (0)
f(x) is continuous at π₯=0
if L.H.L = R.H.L = π(0)
if limβ¬(xβ0^β ) π(π₯)=limβ¬(xβ0^+ ) " " π(π₯)= π(0)
LHL at x β 0
limβ¬(xβ0^β ) f(x) = limβ¬(hβ0) f(0 β h)
= limβ¬(hβ0) f(βh)
= limβ¬(hβ0) (ββ)^2 πππβ‘γπ/((βπ))γ
= limβ¬(hβ0) β^2 π
= 02 .π
= 0
RHL at x β 0
limβ¬(xβ0^+ ) f(x) = limβ¬(hβ0) f(0 + h)
= limβ¬(hβ0) f(h)
= limβ¬(hβ0) β^2 πππβ‘γπ/πγ
= limβ¬(hβ0) β^2 π
= 02. π
= 0
Since,
L.H.L = R.H.L = π(0)
0=π(0)
β΄ f (0) =π
So, the correct answer is (A)

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, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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