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CBSE Class 12-science Answered

Which one of the following method will be correct ? Q. Is the function defined by f (x) =|x| , a continuous function ?
Asked by ritikabehera01 | 13 Mar, 2019, 01:27: PM
answered-by-expert Expert Answer
the given function f(x) = |x| can be expressed as
 
f(x) = x   when x>0
      = -x  when x<0
 
f(x) is continuous at x=0 , because  begin mathsize 12px style limit as x rightwards arrow 0 of space f left parenthesis x right parenthesis space end style exisit
 
let ε << 1   ,  begin mathsize 12px style limit as x rightwards arrow plus epsilon of space f left parenthesis x right parenthesis space space equals space epsilon end style   and  begin mathsize 12px style limit as x rightwards arrow negative epsilon of space f left parenthesis x right parenthesis space space equals space epsilon end style 
 
Left side limit and right side limit are same. Hence f(x) is continuous  at x = 0
Answered by Thiyagarajan K | 13 Mar, 2019, 03:54: PM

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