We have, lim_x→ 232xx^3 8 This is the 00 form.So, apply L hospital rule lim_x→ 2323x^2 0 =323× 2^2 =83 Hence, this is the answer. ...

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Algebra of Limits

limx→ 2∑ 32x/...

Question

${lim}_{x \to 2} \frac{\sum 32 x}{x^{3} - p}$

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Solution

We have,
${lim}_{x \to 2} \frac{32 x}{x^{3} - 8}$

This is the $\frac{0}{0}$ form.
So, apply L-hospital rule
${lim}_{x \to 2} \frac{32}{3 x^{2} - 0}$
$= \frac{32}{3 \times 2^{2}}$
$= \frac{8}{3}$

Hence, this is the answer.

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