Chapter 1: Q. 56 (page 149)

Calculate each limit in Exercises 35–80.
$\underset{x \to \infty}{l i m} \frac{x^{\frac{7}{2}} - x^{\frac{8}{3}}}{x^{2}}$

Short Answer

Expert verified

The limit is infinity.

Step by step solution

Step 1. Given information

The given expression is $\underset{x \to \infty}{l i m} \frac{x^{\frac{7}{2}} - x^{\frac{8}{3}}}{x^{2}}$

Step 2. Calculation

The limit is calculated as below using L'Hopital Rule,

$\underset{x \to \infty}{l i m} \frac{x^{\frac{7}{2}} - x^{\frac{8}{3}}}{x^{2}} = \underset{x \to \infty}{l i m} (\frac{\frac{7}{2} x^{\frac{5}{2}} - \frac{8}{3} x^{\frac{5}{3}}}{2 x}) (differentiating the numerator and denominator) = \underset{x \to \infty}{l i m} (\frac{\frac{35}{4} x^{\frac{3}{2}} - \frac{45}{9} x^{\frac{2}{3}}}{2}) (differentiating the numerator and denominator) = (\frac{\frac{35}{4} {(\infty)}^{\frac{3}{2}} - \frac{45}{9} {(\infty)}^{\frac{2}{3}}}{2}) = \frac{\infty - \infty}{2} = \infty$

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Calculate each limit in Exercises 35–80.
$\underset{x \to \infty}{l i m} \frac{x^{\frac{7}{2}} - x^{\frac{8}{3}}}{x^{2}}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

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Calculate each limit in Exercises 35–80.limx→∞x72-x83x2

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

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Calculate each limit in Exercises 35–80.
$\underset{x \to \infty}{l i m} \frac{x^{\frac{7}{2}} - x^{\frac{8}{3}}}{x^{2}}$