If f(x)={(kx/(|x|), if  x<0 , 3 if  x≥0)} is continuous at x=0, then the value of k is

(a) -3                (b) 0                 (c) 3              (d) any real number

This question is similar to Ex 5.1, 28 - Chapter 5 Class 12




Given that function is continuous at π‘₯=0 𝑓 is continuous at x =0 If L.H.L = R.H.L = 𝑓(0) i.e. lim┬(xβ†’0^βˆ’ ) 𝑓(π‘₯)=lim┬(xβ†’0^+ ) " " 𝑓(π‘₯)= 𝑓(0) LHL at x β†’ 0 (π‘™π‘–π‘š)┬(π‘₯β†’0^βˆ’ ) f(x) = (π‘™π‘–π‘š)┬(β„Žβ†’0) f(0 βˆ’ h) = lim┬(hβ†’0) (π‘˜(0 βˆ’β„Ž))/(|0βˆ’h|) = lim┬(hβ†’0) (π‘˜( βˆ’β„Ž))/h = -k Since L.H.L = R.H.L βˆ’π‘˜=3 π’Œ= βˆ’πŸ‘

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Davneet Singh

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.