Say true or false: (i)   f(x) =  [ x ] is continuous over the interval [ 1 , 2 ]. (ii)  g(x) = 1/x  for x > 0 and g(0) = 0 is continuous over [0 , 1 ].  

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Say true or false:

(i)   f(x) =  [ x ] is continuous over the interval [ 1 , 2 ].

(ii)  g(x) = 1/x  for x > 0 and g(0) = 0 is continuous over [0 , 1 ].

(i) false: `lim_(x->2^(-))f(x)=1` but `f(2)=2` . (The function is continuous on (1,2) ).

(ii) False: `lim_(x->0^+)= oo` , or the limit fails to exist. It certainly does not equal f(0).

 

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