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Algebra of Limits

Show that l...

Question

Show that $\begin{matrix} lim x \to 0 \end{matrix} (\frac{x^{5} + 2 x^{4} + x^{2} + 3 x + 2}{x^{4} + {2 x}^{3} + {3 x}^{2} - 5 x - 22}) = - \frac{1}{11}$

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Solution

Given,
${lim}_{x \to 0} (\frac{x^{5} + 2 x^{4} + x^{2} + 3 x + 2}{x^{4} + 2 x^{3} + 3 x^{2} - 5 x - 22})$
$= \frac{0^{5} + 2 \cdot 0^{4} + 0^{2} + 3 \cdot 0 + 2}{0^{4} + 2 \cdot 0^{3} + 3 \cdot 0^{2} - 5 \cdot 0 - 22}$
$= \frac{2}{- 22}$
$= - \frac{1}{11}$

Hence, this is the answer.

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