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  • Evaluate the following: <img alt="\lim_{x\rightarrow 0}\frac{r}{x^{n}}\log \left ( 1+x^{n} \right )" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Clim_%7Bx%5Crightarrow%200%7D%5Cfrac%7Br%

Evaluate the following: \lim_{x\rightarrow 0}\frac{r}{x^{n}}\log \left ( 1+x^{n} \right )

Option: 1

1


Option: 2

0


Option: 3

e


Option: 4

r


Answers (1)

best_answer

Given: \lim_{x\rightarrow 0}\frac{r}{x^{n}}\log \left ( 1+x^{n} \right )

Use the power rule of logarithmic \log_{e}a^{b}= b \log_{e}a.

= \lim_{x\rightarrow 0}r \log \left ( 1+x^{n} \right )^{\frac{1}{x^{n}}}

Using the property of the limit = \lim_{x\rightarrow a}\left ( 1+x \right )^{\frac{1}{x}}= e,

= \lim_{x\rightarrow a}r \log e
The value of \log e is 1 .

= r\left ( 1 \right )
= r
Therefore,\lim_{x\rightarrow 0}\frac{r}{x^{n}}\log \left ( 1+x^{n} \right )= r.

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avinash.dongre

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