Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Question

Answered step-by-step

Find the limit or show that it does not exist.

$ \displaystyle \lim_{x \to \infty} (e^{-x} + 2 \cos 3x) $

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Ma. Theresa Alin

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

02:51

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 6

Limits at Infinity: Horizontal Asymptotes

Limits

Derivatives

Campbell University

University of Nottingham

Boston College

Lectures

04:40

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

0:00

Find the limit or show tha…

07:25

03:08

02:39

01:16

Find the limit, if it exis…

01:29

01:52

01:06

Find the given limit, or s…

01:07

to evaluate the limits of erase the negative X. Plus to co sign of three X. As X approaches infinity, we first write this into the limit as X approaches infinity of erase the negative X. Plus you have a limit as X approaches infinity Of to co sign of three x. Now evaluating the first limit we have erased negative infinity Plus we have rewriting the second limit. That's too the limit. As X approaches infinity of Co sign of three x. Note that co sign function is a periodic function and we know that the value of co sign range is from negative 1 to 1. That means co sign of X. This is greater than or equal to negative one But this is less or equal to one. And because this is periodic The Value of Co Sign of three X. As X gets larger and larger Will either be -1 or one. and because the value of coastline of three x approaches to two values -1 or one. Then the value of the whole limit is indeterminate. That means it does not exist. In order to have a limit, we only need one value

View More Answers From This Book

Find Another Textbook

00:55

Suppose f(r) is function with critical point at € = 2. The graph of the seco…

00:57

Find the missing factor in the following expression _ 32+h =32(_)32+h = …

03:18

point) Let &n 79 (n 5 1)9. Let Sndn n=3ka) Find S3 Sz 19683(…

05:23

w =Xy +Yz + ZX, X=r Cos(0) , Y = r sin(0) , 2 = r8; Dw Dw when r = 4, 0 = dr…

06:43

of a circle is Increasing at a rate of 4 centimeters per minute: Find the ra…

01:01

(1 point) IQ scores have a mean Of 100 and a standard deviation Of 15. Pam h…

10 pEsQuestion 13Acoin is flipped, dice is rolled and card Is drawn …

In a lottery; player selects 3 different numbers out of a possible 40. What …

03:06

A major issue facing many states is whether to legalize casino gambling: Sup…

04:33

Question 62 ptsThe manager of an online shop wants to determine whet…