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Standard Limits to Remove Indeterminate Form

lim x → 0log|...

Question

${lim}_{x \to 0} \frac{l o g | 1 + x^{3} |}{s i n^{3} x}$

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Solution

${lim}_{x \to 0} \frac{l o g | 1 + x^{3} |}{s i n^{3} x}$

$= {lim}_{x \to 0} \frac{l o g | 1 + x^{3} |}{x^{3}} \times \frac{1}{{lim}_{x \to 0} {(\frac{s i n x}{x})}^{3}}$

$= 1 \times 1$

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