/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 23 Determine the following limits. ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 23

Determine the following limits. $$\lim _{x \rightarrow \infty}\left(-12 x^{-5}\right)$$

Short Answer

Expert verified
Question: Determine the limit of the function $$f(x) = -12x^{-5}$$ as $$x$$ tends to infinity. Answer: $$\lim _{x \rightarrow \infty}\left(-\frac{12}{x^5}\right) = 0$$

Step by step solution

01

Rewrite the function

We can rewrite the given function as $$f(x) = -12x^{-5} = -\frac{12}{x^5}$$ to make the manipulation easier.
02

Check the behavior of the function for large x values

As $$x$$ tends to infinity, the denominator, $$x^5$$, will grow to a very large number. Since the numerator, -12, remains constant, the overall value of the function will become very small (i.e., it will approach to 0).
03

Determine the limit

Based on the observation in the previous step, we can conclude that as $$x$$ tends to infinity, the function approaches 0. Therefore, the limit is: $$\lim _{x \rightarrow \infty}\left(-\frac{12}{x^5}\right) = 0$$

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

a. Evaluate \(\lim _{x \rightarrow \infty} f(x)\) and \(\lim _{x \rightarrow-\infty} f(x),\) and then identify any horizontal asymptotes. b. Find the vertical asymptotes. For each vertical asymptote \(x=a\), evaluate \(\lim _{x \rightarrow a^{-}} f(x)\) and \(\lim _{x \rightarrow a^{+}} f(x)\). $$f(x)=\frac{\left|1-x^{2}\right|}{x(x+1)}$$

Let $$g(x)=\left\\{\begin{array}{ll}1 & \text { if } x \geq 0 \\\\-1 & \text { if } x<0\end{array}\right.$$ a. Write a formula for \(|g(x)|\) b. Is \(g\) continuous at \(x=0 ?\) Explain. c. Is \(|g|\) continuous at \(x=0 ?\) Explain. d. For any function \(f,\) if \(|f|\) is continuous at \(a,\) does it necessarily follow that \(f\) is continuous at \(a ?\) Explain.

Torricelli's Law A cylindrical tank is filled with water to a depth of 9 meters. At \(t=0,\) a drain in the bottom of the tank is opened and water flows out of the tank. The depth of water in the tank (measured from the bottom of the tank) \(t\) seconds after the drain is opened is approximated by \(d(t)=(3-0.015 t)^{2},\) for \(0 \leq t \leq 200\). Evaluate and interpret \(\lim _{t \rightarrow 200^{-}} d(t)\).

Classify the discontinuities in the following functions at the given points. See Exercises \(91-92.\) $$h(x)=\frac{x^{3}-4 x^{2}+4 x}{x(x-1)} ; x=0 \text { and } x=1$$

a. Evaluate \(\lim _{x \rightarrow \infty} f(x)\) and \(\lim _{x \rightarrow-\infty} f(x),\) and then identify any horizontal asymptotes. b. Find the vertical asymptotes. For each vertical asymptote \(x=a\), evaluate \(\lim _{x \rightarrow a^{-}} f(x)\) and \(\lim _{x \rightarrow a^{+}} f(x)\). $$f(x)=\frac{\sqrt{16 x^{4}+64 x^{2}}+x^{2}}{2 x^{2}-4}$$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.