Chapter 7: Q. 5 (page 639)

Let $r (x)$ be a nonzero rational function. Evaluate $\lim_{x \to \infty} \frac{r (x + 1)}{r (x)}$ .

Short Answer

Expert verified

The answer is $1 .$

Step by step solution

Step 1. Given information.

It is given to evaluate $\lim_{x \to \infty} \frac{r (x + 1)}{r (x)}$ .

Step 2. Required Value.

Now,

$r (x + 1) = \sum_{i = 0}^{\infty} \frac{a_{i}}{b_{i}} (x + 1)^{i} \frac{r (x + 1)}{r (x)} = \frac{\frac{a_{i}}{b_{i}} (x + 1)^{'}}{\frac{a_{i}}{b_{i}} x^{i}} = \frac{(x + 1)^{i}}{x^{i}} = {(1 + \frac{1}{x})}^{i}$

Applying limit,

$\lim_{x \to \infty} \frac{r (x + 1)}{r (x)} = \lim_{x \to \infty} {(1 + \frac{1}{x})}^{'} = \lim_{x \to \infty} (1 + 0)^{i} = 1$

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Let $r (x)$ be a nonzero rational function. Evaluate $\lim_{x \to \infty} \frac{r (x + 1)}{r (x)}$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Required Value.

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Letr(x)be a nonzero rational function. Evaluate limx→∞r(x+1)r(x).

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Required Value.

One App. One Place for Learning.

Most popular questions from this chapter

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Let $r (x)$ be a nonzero rational function. Evaluate $\lim_{x \to \infty} \frac{r (x + 1)}{r (x)}$ .