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Chapter 1: Q. 40 (page 149)

Calculate each limit in Exercises 35-80.
$\lim_{x \to \infty} (x^{4} - x^{5})$

Short Answer

Expert verified

The limit of the function is $\lim_{x \to \infty} (x^{4} - x^{5}) = - \infty$ .

Step by step solution

01

Step 1. Given information.

We have:

$\lim_{x \to \infty} (x^{4} - x^{5})$

02

Step 2. Find the limits.

The function is $\lim_{x \to \infty} (x^{4} - x^{5})$ .

Apply infinity property: $\lim_{x \to \infty} (a x^{n} + \dots + b x + c) = - \infty, a < 0, n is odd$

$a = - 1, n = 5 = - \infty$

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Most popular questions from this chapter

Write each of the inequalities in interval notation:

$|(x^{2} - 1) + 3| < 0.5$

Write a delta–epsilon proof that proves that $f$ is continuous on its domain. In each case, you will need to assume that δ is less than or equal to $1$ .

$f (x) = x^{3}$

$\lim_{x \to 0} (\frac{2 x}{e^{x} - 1})$

Sketch a labeled graph of a function that fails to satisfy the hypothesis of the Extreme Value Theorem, and illustrate on your graph that the conclusion of the Extreme Value Theorem does not necessarily hold.

Write each of the inequalities in interval notation:

$0 < | x - 2 | < 0.1$

See all solutions

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