If f and g are both continuous at x = a, then f-g is

If f'(x) = g(x) (x-a)^2 , where g(a) != 0 and g is continuous at x = a, then :

Let f(x)=[x], where [.] is the greatest integer fraction and g(x)=sin x be two valued functions over R. Which of the following statements is correct? (a) Both f(x) and g(x) are continuous at x=0 (b) f(x) is continuous at x=0, but g(x) is not continuous at x=0. (c) g(x) is continuous at x=0, but f(x) is not continuous at x=0. (d) Both f(x) and g(x) are discontinuous at x=0

If f and g are two continuous functions on their common domain D then f.g and (f)/(g) is continuous on D provided g(x) is defined at that point.

If f.g is continuous at x = 0 , then f and g are separately continuous at x = 0 .

If f.g is continuous at x = 0 , then f and g are separately continuous at x = 0 .

If f.g is continuous at x = 0 , then f and g are separately continuous at x = 0 .

If f and g are two continuous functions on their common domain D then f+g and f-g is continuous on D.

If f'(x)=g(x)(x-a)^(2), where g(a)!=0 and g is continuous at x=a, then :

If f.g is continuous at x=a, then f and g are separately continuous at x= a.