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  • denotes the fractional part of a real no. <img alt="\mathrm{x}" src="https://entrancecorner.o

\mathrm{{x}} denotes the fractional part of a real no. \mathrm{x}, then \mathrm{\lim _{x \rightarrow 0}\left\{\frac{\ln (1+\{x\})}{\{x\}}\right\}} is
 

Option: 1

0


Option: 2

-1


Option: 3

1


Option: 4

non-existent.


Answers (1)

best_answer

Let \mathrm{ f(x)=\frac{\ln (1+|x|)}{|x|} }

\mathrm{ f(0+h)=\frac{\ln (1+h)}{h} }

\mathrm{ f(0+0)=1 }               .........(1)

\mathrm{ \Rightarrow f(0-h)=\frac{\ln {1+\{-h })}{|-h|}=\frac{\ln (1-h+1)}{-h+1} }

\mathrm{ \Rightarrow f(0-0)=\ln 2 }        ...........(2)

\mathrm{ \because f(0+0) \neq f(0-0) }

\mathrm{ \Rightarrow \lim _{x \rightarrow 0} f(x)}does not exist.
Hence option 4 is correct.

Posted by

Ritika Kankaria

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