# Ex 5.1, 24 - Chapter 5 Class 12 Continuity and Differentiability

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Ex 5.1, 24 Determine if f defined by 𝑓 𝑥= 𝑥2 sin 1𝑥, 𝑖𝑓 𝑥≠0&0, 𝑖𝑓 𝑥=0 is a continuous function? 𝑓 𝑥= 𝑥2 sin 1𝑥, 𝑖𝑓 𝑥≠0&0, 𝑖𝑓 𝑥=0 At x = 0 A function is continuous at x = 0 if L.H.L = R.H.L = 𝑓 0 i.e. limx→ 0− 𝑓 𝑥= limx→ 0+ 𝑓 𝑥= 𝑓 0 L.H.L limx→ 0− 𝑓 𝑥 = limx→ 0− 𝑥2 sin 1𝑥 Putting 𝑥 = 0 − ℎ = limℎ→0 0−h2 . sin 10 − ℎ = limℎ→0 −h2 . sin 1− ℎ = limℎ→0 ℎ2 . sin 1− ℎ = limℎ→0 − ℎ2 . sin . 1ℎ = limℎ→0 − ℎ2 . 𝑘 Putting h = 0 = 02. 𝑘 = 0 ∴ LHL = 0 R.H.L limx→ 0+ 𝑓 𝑥 = limx→ 0+ 𝑥2 sin 1𝑥 Putting 𝑥 = 0+ℎ = limℎ→0 0+h2 . sin 10 + ℎ = limℎ→0 ℎ2 . sin 1ℎ = limℎ→0 ℎ2 . 𝑘 Putting h = 0 = 02. 𝑘 = 0 & 𝑓 0 = 0 Thus L.H.L = R.H.L = 𝑓 0 Hence 𝒇 𝒙 is continuous for all real value of 𝒙 .

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.