NDA Math Limit, Continuity and Differentiability

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Consider the following for the next three (03) items that follow:
Let f(x)=[x], where [.] is the greatest integer function andg(x)=sinx be two real valued functions over R

[NDA II 2016]

Question : 57 of 105

Marks: +1, -0

Which of the following statements is correct ?

[NDA II 2016]

Both f(x) and g(x) are continuous at x=0.
f(x) is continuous at x=0, but g(x) is not continuous at x=0.
g(x) is continuous at x = 0, but f(x) is not continuous at x=0.
Both f(x) and g(x) are discontinuous at x=0

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