Explanation Given: The function is given as: f ( x ) = 3 x ( x + 2 ) 3 Formula used: lim x → a f ( x ) = f ( a ) Calculation: The value of lim x → − 2 3 x ( x + 2 ) 3 cannot be found out by application of the polynomial limit which is, lim x → a f ( x ) = f ( a ) . Neither the quotient rule be applied as lim x → − 2 ( x + 2 ) 3 = 0 , an irregularity is created. Try to convert the limit into a simpler form to remove the irregularity. lim x → − 2 3 x ( x + 2 ) 3 = lim x → − 2 3 x ( x + 2 ) ( x + 2 ) ( x + 2 ) As this function cannot be solved further, thus the limit will give the value ∞ after application of polynomial limit rule

12th Edition

ISBN: 8220106844557

Author: MULLINS

Publisher: PEARSON

See similar textbooks

Concept explainers

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …

Videos

Question

Chapter 11.1, Problem 46E

To determine

To calculate: The value of limit of the function f(x)=3x(x+2)3

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.1, Problem 45E

Chapter 11.1, Problem 47E

Students have asked these similar questions

A major company in the Montreal area, offering a range of engineering services from project preparation to construction execution, and industrial project management, wants to ensure that the individuals who are responsible for project cost estimation and bid preparation demonstrate a certain uniformity in their estimates. The head of civil engineering and municipal services decided to structure an experimental plan to detect if there could be significant differences in project evaluation. Seven projects were selected, each of which had to be evaluated by each of the two estimators, with the order of the projects submitted being random. The obtained estimates are presented in the table below. a) Complete the table above by calculating: i. The differences (A-B) ii. The sum of the differences iii. The mean of the differences iv. The standard deviation of the differences b) What is the value of the t-statistic? c) What is the critical t-value for this test at a significance level of 1%?…

In the graph provided, triangle N'O'P' is the image of triangle NOP after a dilation. 104 -9- -8- 7 6 N 5 0 -4- N 3 2 1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 p -5 -6 -7 -8 X

mv2 The centripetal force of an object of mass m is given by F (r) = rotation and r is the distance from the center of rotation. ' where v is the speed of r a. Find the rate of change of centripetal force with respect to the distance from the center of rotation. F(r) b. Find the rate of change of centripetal force of an object with mass 500 kilograms, velocity of 13.86 m/s, and a distance from the center of rotation of 300 meters. Round to 2 decimal places. N/m (or kg/s²) F' (300)

Chapter 11 Solutions

EBK MATHEMATICS WITH APPLICATIONS IN TH

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The value of limit of the function f ( x ) = 3 x ( x + 2 ) 3

Concept explainers

Videos

To calculate: The value of limit of the function f(x)=3x(x+2)3

Want to see the full answer?

Chapter 11 Solutions