Chapter 1: Q. 14 (page 152)

Suppose $\frac{p (x)}{q (x)}$ is a rational function with deg $(p (x))$ $= n$ and $d e g (q (x))$ $= m,$ if $n < m$ then, $\lim_{x \to \infty} \frac{p (x)}{q (x)} = ?,$ if $n = m,$ then $\lim_{x \to \infty} \frac{p (x)}{q (x)} = ?,$ and if $n > m, t h e n \lim_{x \to \infty} \frac{p (x)}{q (x)} = ? .$

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Expert verified

Suppose $\frac{p (x)}{q (x)}$ is a rational function with $d e g (p (x)) = n a n d d e g (q (x)) = m$ , if $n < m, t h e n \lim_{x \to \infty} \frac{p (x)}{q (x)} = 0, i f n = m, t h e n \lim_{x \to \infty} \frac{p (x)}{q (x)} = \frac{a_{n}}{b_{m}}$ , and if $n > m$ , then $\lim_{x \to \infty} \frac{p (x)}{q (x)} = n o t d e f i n e d .$

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Step 1. Given Information.

The given statement is ,

Suppose $\frac{p (x)}{q (x)}$ is a rational function withlocalid="1648279271694" $d e g (p (x)) = n and deg (q (x)) = m, if n < m then, \lim_{x \to \infty} \frac{p (x)}{q (x)} = ?, if n = m, then \lim_{x \to \infty} \frac{p (x)}{q (x)} = ?, and if n > m, then \lim_{x \to \infty} \frac{p (x)}{q (x)} = ?$

Step 2. Fill the blanks.

Suppose $\frac{p (x)}{q (x)}$ is a rational function with $deg (p (x)) = n and deg (q (x)) = m, if n < m, then \lim_{x \to \infty} \frac{p (x)}{q (x)} = 0, if n = m, then \lim_{x \to \infty} \frac{p (x)}{q (x)} = \frac{a_{n}}{b_{m}}, and if n > m, then \lim_{x \to \infty} \frac{p (x)}{q (x)} = not de fined$

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Supposep(x)q(x)is a rational function with deg(p(x))=nanddeg(q(x))=m,if n<mthen,limx→∞p(x)q(x)=?,if n=m,thenlimx→∞p(x)q(x)=?,and if n>m,thenlimx→∞p(x)q(x)=?.

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Step by step solution

Step 1. Given Information.

Step 2. Fill the blanks.

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