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Question 4 - CBSE Class 12 Sample Paper for 2024 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at Aug. 14, 2023 by

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

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Transcript

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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