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 : 58 of 105

Marks: +1, -0

Which one of the following statements is correct?

[NDA II 2016]

lim
x→0
(fog)(x) exists
lim
x→0
(gof)(x) exists
lim
x→0+
(‌fog‌)(x)=
lim
x→0−
(gof(x)
lim
x→0+
(‌fog‌)(x)=
lim
x→0+
(gof(x)

Validate

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