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  • Assertion: <img alt="\mathrm[\lim _{n \rightarrow 0} \frac{\log (1+n)}{n}=1]" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%5B%5Clim%20_%7Bn%20%5Crightarrow%200%7D%20%5Cfrac%7B%5Cl

Assertion: \mathrm[\lim _{n \rightarrow 0} \frac{\log (1+n)}{n}=1]

Reason: The value of limit  \mathrm{\lim _{n \rightarrow 0} \frac{\log (1+n)}{n}=1} can be found using taylor’s expansion.

 

Option: 1

Assertion and Reason both are correct statements and reason is the correct explanation for assertion.
 

 


Option: 2

Assertion and Reason both are correct statements and reason is not the correct explanation for assertion.


Option: 3

Assertion is correct and reason is wrong.

 


Option: 4

Assertion is wrong but reason is correct.


Answers (1)

\mathrm{ \lim _{x \rightarrow 0} \frac{\log _e(1+x)}{x}=\lim _{x \rightarrow 0} \frac{x-\frac{x^2}{2}+\frac{x^3}{3}-\cdots}{x} }
[using Taylor series expansion of \mathrm{\left.\log _e(1+x)\right]}

\mathrm{ \begin{aligned} & =\lim _{x \rightarrow 0}\left(1-\frac{x}{2}+\frac{x^2}{3}-\cdots\right) \\ & =1 \end{aligned} }
 

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Kshitij

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