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  • Evaluate given limit: <img alt="\lim _{x \rightarrow \infty} \frac{\sqrt{21} x^{11}-\sqrt{43} x^2-58 x}{\sqrt{3} x^{11}+\sqrt{67} x-37}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Clim%

Evaluate given limit: \lim _{x \rightarrow \infty} \frac{\sqrt{21} x^{11}-\sqrt{43} x^2-58 x}{\sqrt{3} x^{11}+\sqrt{67} x-37}

Option: 1

\sqrt{7}


Option: 2

\sqrt{14}


Option: 3

\sqrt{21}


Option: 4

\sqrt{28}


Answers (1)

best_answer

\lim _{x \rightarrow \infty} \frac{\sqrt{21} x^{11}-\sqrt{43} x^2-58 x}{\sqrt{3} x^{11}+\sqrt{67} x-37}

This expression can also be written as

=\lim _{x \rightarrow \infty} \frac{\sqrt{21} x^{11}\left(1-\frac{\sqrt{43}}{\sqrt{21} x^9}-\frac{58}{\sqrt{21} x^{10}}\right)}{\sqrt{3} x^{11}\left(1+\frac{\sqrt{67}}{\sqrt{3} x^{10}}-\frac{37}{\sqrt{3} x^{11}}\right)}

=\lim _{x \rightarrow \infty} \frac{\sqrt{21}\left(1-\frac{\sqrt{43}}{\sqrt{21} x^9}-\frac{58}{\sqrt{21} x^{10}}\right)}{\sqrt{3}\left(1+\frac{\sqrt{67}}{\sqrt{3} x^{10}}-\frac{37}{\sqrt{3} x^{11}}\right)}

Putting value of limit:

\begin{aligned} & =\frac{\sqrt{21}(1)}{\sqrt{3}(1)} \\ & =\sqrt{7} \end{aligned}

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Sayak

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