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Phrases Continuity PYQ



Test the continuity of the function at x = 2 
f(x)={52x if x<21 if x=2x32 if x>2





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Solution

LHL ≠ f(2)


Let  ,where [x]denotes the greatest integer





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Solution



f(x)=x+|x| is continuous for





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Solution



If f:RR is defined by f(x)={x+2x2+3x+2,ifxR{1,2}1,ifx=20,ifx=1 , then f(x) is continuous on the set 





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Solution



 is continuous for





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Solution



Let g:RR and h:RR, be two functions such that h(x)=sgn(g(x)). Then select which of the following is not true?( R denotes the set of all real numbers, sgn stands for signum function)





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Solution



If  is a continuous function at x = 0, then the value of k is





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Solution



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