The process by which we determine limits of rational functions applies equally well to ratios containing noninteger or negative powers of x

usagirl007A 2021-09-13 Answered

The process by which we determine limits of rational functions applies equally well to ratios containing noninteger or negative powers of x: Divide numerator and denominator by the highest power of x in the denominator and proceed from there. Find the limits. \(\lim_{x \to \infty} \frac{((x^{-1})+(x^{-4}))}{((x^{-2})-(x^{-3}))}\)

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timbalemX
Answered 2021-09-14 Author has 19964 answers

\(\displaystyle{x}^{{-{{2}}}}\) is highest power of x in denominator. Dividing with \(x^{-2}\) is same as multiplying numerator and denominator with \(\displaystyle{x}^{{2}}\). ​

\(\lim_{x \to \infty} \frac{(x^{-1})+(x^{-4}))}{((x^{-2})−(x^{-3}))} \cdot \frac{(x^2)}{(x^2)}=\lim_{x \to \infty} \frac{(x+x^{-2})}{(1-x^{-1})}=\)

Use that \(\lim_{x \to \infty} x^{-n}=0 = \frac{(\infty+0)}{(1-0)}=\infty\)

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