We have an answer to "Find the limit: limx→∞(1−x3x2+7x)5"

shadsiei

Answered question

2021-10-15

Find the limit:

lim_{x \to \infty} {(\frac{1 - x^{3}}{x^{2} + 7 x})}^{5}

Answer & Explanation

sovienesY

Skilled2021-10-16Added 89 answers

The given limit expression is $lim_{x \to - \infty} ({(\frac{1 - x^{3}}{x^{2} + 7 x})}^{5})$
Find the limit as follows:
$lim_{x \to - \infty} ({(\frac{1 - x^{3}}{x^{2} + 7 x})}^{5}) = {(lim_{x \to - \infty} (\frac{1 - x^{3}}{x^{2} + 7 x}))}^{5}$
$= {(lim_{x \to - \infty} (\frac{\frac{1}{x^{2}} - \frac{x^{3}}{x^{2}}}{\frac{x^{2}}{x^{2}} + \frac{7 x}{x^{2}}}))}^{5}$
$= (lim_{x \to - \infty} {(\frac{\frac{1}{x^{2}} - x}{1 + \frac{7}{x}})}^{5}$
$= (\frac{lim_{x \to - \infty} (\frac{1}{x^{2}} - x)}{lim_{x \to - \infty} (1 + \frac{7}{x})})$
$= {(\frac{\infty}{1})}^{5}$
$= \infty$

Jeffrey Jordon

Expert2022-08-30Added 2575 answers

Answer is given below (on video)

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