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Let $\mathrm{f}(\mathrm{x})=[\mathrm{x}]$, where $[.]$ is the greatest integer function and $\mathrm{g}(\mathrm{x})=\sin \mathrm{x}$ be two real valued functions over R.
Which of the following statements is correct?
Options:
Which of the following statements is correct?
Solution:
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Verified Answer
The correct answer is:
$\mathrm{g}(\mathrm{x})$ is continuous at $\mathrm{x}=0$, but $\mathrm{f}(\mathrm{x})$ is not continuous at $\mathrm{x}=0 .$
$f(x)=[x]$ and $g(x)=\sin x$ $\lim _{x \rightarrow 0^{+}} f(x)=[0+h]=0$
$\lim _{x \rightarrow 0^{-}} f(x)=[0-h]=-1$
$f(0)=0$
$\Rightarrow f(x)$ is not continuous at $x=0$ and also $g(x)$ is
continuous at $x=0$. (every trignometric function is continuous).
$\lim _{x \rightarrow 0^{-}} f(x)=[0-h]=-1$
$f(0)=0$
$\Rightarrow f(x)$ is not continuous at $x=0$ and also $g(x)$ is
continuous at $x=0$. (every trignometric function is continuous).
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