Explanation Result used: The limit of the function lim x → 0 | x | x = 1 . The function f is continuous at a , but not differentiable at a. Because, the right and left derivatives of a function are not equal. The differentiable function is continuous. But, the continuous function need not be continuous. Description: Every continuous function need not be a differentiable function. For example, the function f ( x ) = | x | is continuous at 0 but it is not differentiable at 0. The derivative f ( x ) = | x | at x = 0 is lim h → 0 f ( 0 + h ) − f ( 0 ) h . Left side limit is calculated as follows. lim h → 0 − f ( 0 + h ) − f ( 0 ) h = lim h → 0 − | 0 + h | − | 0 | h = lim h → 0 − | 0 + h | − | 0 | h = lim h → 0 − | h | h Since the value of h approaches 0 from left, so h is a negative value. The absolute value of h is | h | = − h . lim h → 0 − f ( 0 + h ) − f ( 0 ) h = lim h → 0 − − h h = − 1 Thus, the left side limit is − 1 . Right side limit is calculated as follows. lim h → 0 + f ( 0 + h ) − f ( 0 ) h = lim h → 0 + | 0 + h | − | 0 | h = lim h → 0 + | 0 + h | − | 0 | h = lim h → 0 + | h | h Since the value of h approaches 0 from right, so h is a positive value

11th Edition

ISBN: 2818440028625

Author: Lial

Publisher: ELSEVIER

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 3, Problem 14RE

To determine

To explain: Whether every continuous function is differentiable or not and every differentiable function is continuous or not.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 3, Problem 13RE

Chapter 3, Problem 15RE

Students have asked these similar questions

Inverse laplace transform Lect: Huda I H.w 1- F(S)= A- Find - F(s) of the following S (s+1)5 1 2- F(s) s² (s-a) 5+5 3- F(s)= s2+4s+3 1 4- F(s)= (s+2)2(s-2) 3s2-7s+5 5- F(s)= (s-1)(s2-5s+6)

Inverse laplace transform Lect :Huda I H.w A- Find L-1 F(s) of the following 1- F(S)= 2- F(s)- S (+1)5 s² (s-a) 5+5 s2+4s+3 3- F(s)- 1 4- F(s)- (s+2)2(s-2) 3s2-7s+5 5- F(s)- (s-1)(s2-55+6) B-Solve the D.E of the following: 1- y'+3y+2fy dt = f(t) for y(0)-1 if f(t) is the function whose graph is shown below 2 1 2 2-y+4y-u(t) for y(0)=y'(0)=0 3- y"+4y'+13y= e−2t sin3t for y(0)-1 and y'(0)=-2 17

show step by step answer

Chapter 3 Solutions

CALCULUS WITH APPLICATIONS

Ch. 3.1 - YOUR TURN 1 Find . Ch. 3.1 - YOUR TURN 2 Find . Ch. 3.1 - Prob. 3YT Ch. 3.1 - YOUR TURN 4 Find . Ch. 3.1 - YOUR TURN 5 Find . Ch. 3.1 - YOUR TURN 6 Find . Ch. 3.1 - Prob. 7YT Ch. 3.1 - Prob. 8YT Ch. 3.1 - Prob. 1WE Ch. 3.1 - Prob. 2WE

Ch. 3.1 - Prob. 3WE Ch. 3.1 - Prob. 4WE Ch. 3.1 - In Exercises 1-4, choose the best answer for each...Ch. 3.1 - In Exercises 1-4, choose the best answer for each...Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Decide whether each limit exists. If a limit...Ch. 3.1 - Decide whether each limit exists. If a limit...Ch. 3.1 - Prob. 7E Ch. 3.1 - Decide whether each limit exists. If a limit...Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E Ch. 3.1 - Decide whether each limit exists. If a limit...Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - 14. In Exercise 10, why does , even though f(1) =...Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Complete the tables and use the results to find...Ch. 3.1 - Complete the tables and use the results to find...Ch. 3.1 - Complete the tables and use the results to find...Ch. 3.1 - Prob. 21E Ch. 3.1 - Let and . Use the limit rules to find each...Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Let and . Use the limit rules to find each...Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Use the properties of limits to help decide...Ch. 3.1 - Use the properties of limits to help decide...Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 34E Ch. 3.1 - Use the properties of limits to help decide...Ch. 3.1 - Prob. 36E Ch. 3.1 - Use the properties of limits to help decide...Ch. 3.1 - Use the properties of limits to help decide...Ch. 3.1 - Prob. 39E Ch. 3.1 - Use the properties of limits to help decide...Ch. 3.1 - Prob. 41E Ch. 3.1 - Prob. 42E Ch. 3.1 - Prob. 43E Ch. 3.1 - Use the properties of limits to help decide...Ch. 3.1 - Prob. 45E Ch. 3.1 - Prob. 46E Ch. 3.1 - Prob. 47E Ch. 3.1 - Use the properties of limits to help decide...Ch. 3.1 - Prob. 49E Ch. 3.1 - Use the properties of limits to help decide...Ch. 3.1 - Prob. 51E Ch. 3.1 - Use the properties of limits to help decide...Ch. 3.1 - Prob. 53E Ch. 3.1 - Prob. 54E Ch. 3.1 - Prob. 55E Ch. 3.1 - 56. Let Find Find Ch. 3.1 - 57. Does a value of k exist such that the...Ch. 3.1 - 58. Repeat the instructions of Exercise 57 for the...Ch. 3.1 - Prob. 59E Ch. 3.1 - Prob. 60E Ch. 3.1 - Prob. 61E Ch. 3.1 - Prob. 62E Ch. 3.1 - Prob. 63E Ch. 3.1 - Prob. 64E Ch. 3.1 - Prob. 65E Ch. 3.1 - Prob. 66E Ch. 3.1 - Prob. 67E Ch. 3.1 - Prob. 68E Ch. 3.1 - Prob. 69E Ch. 3.1 - Prob. 70E Ch. 3.1 - Prob. 71E Ch. 3.1 - Prob. 72E Ch. 3.1 - Prob. 73E Ch. 3.1 - Find each of the following limits (a) by...Ch. 3.1 - Prob. 75E Ch. 3.1 - Prob. 76E Ch. 3.1 - Prob. 77E Ch. 3.1 - Prob. 78E Ch. 3.1 - Prob. 79E Ch. 3.1 - Prob. 80E Ch. 3.1 - Prob. 81E Ch. 3.1 - Prob. 82E Ch. 3.1 - Prob. 83E Ch. 3.1 - 84. APPLY IT Consumer Demand When the price of an...Ch. 3.1 - 85. Sales Tax Officials in California tend to...Ch. 3.1 - Prob. 86E Ch. 3.1 - 87. Average Cost The cost (in dollars) for...Ch. 3.1 - Prob. 88E Ch. 3.1 - Prob. 89E Ch. 3.1 - 90. Preferred Stock In business finance, an...Ch. 3.1 - Prob. 91E Ch. 3.1 - Prob. 92E Ch. 3.1 - 93. Sediment To develop strategies to manage water...Ch. 3.1 - Prob. 94E Ch. 3.1 - Prob. 95E Ch. 3.2 - YOUR TURN 1 Find all values x = a where the...Ch. 3.2 - YOUR TURN 2 Find all values of x where the...Ch. 3.2 - Find each of the following limits. W1. Ch. 3.2 - Prob. 2WE Ch. 3.2 - Prob. 3WE Ch. 3.2 - Prob. 4WE Ch. 3.2 - Prob. 5WE Ch. 3.2 - In Exercises 1–6, find all values x = a where the...Ch. 3.2 - In Exercises 1–6, find all values x = a where the...Ch. 3.2 - Prob. 3E Ch. 3.2 - Prob. 4E Ch. 3.2 - In Exercises 1–6, find all values x = a where the...Ch. 3.2 - Prob. 6E Ch. 3.2 - Find all values x = a where the function is...Ch. 3.2 - Find all values x = a where the function is...Ch. 3.2 - Find all values x = a where the function is...Ch. 3.2 - Find all values x = a where the function is...Ch. 3.2 - Prob. 11E Ch. 3.2 - Prob. 12E Ch. 3.2 - Prob. 13E Ch. 3.2 - Find all values x = a where the function is...Ch. 3.2 - Find all values x = a where the function is...Ch. 3.2 - Find all values x = a where the function is...Ch. 3.2 - Find all values x = a where the function is...Ch. 3.2 - Find all values x = a where the function is...Ch. 3.2 - Prob. 19E Ch. 3.2 - In Exercises 19–24, (a) graph the given function,...Ch. 3.2 - In Exercises 19–24, (a) graph the given function,...Ch. 3.2 - In Exercises 19–24, (a) graph the given function,...Ch. 3.2 - Prob. 23E Ch. 3.2 - Prob. 24E Ch. 3.2 - Prob. 25E Ch. 3.2 - In Exercises 25–28, find the value of the constant...Ch. 3.2 - In Exercises 25–28, find the value of the constant...Ch. 3.2 - In Exercises 25–28, find the value of the constant...Ch. 3.2 - Prob. 29E Ch. 3.2 - Prob. 30E Ch. 3.2 - Prob. 31E Ch. 3.2 - Prob. 32E Ch. 3.2 - Prob. 33E Ch. 3.2 - Prob. 34E Ch. 3.2 - 35. Production The graph shows the profit from the...Ch. 3.2 - 36. Cost Analysis The cost to transport a mobile...Ch. 3.2 - Prob. 37E Ch. 3.2 - Prob. 38E Ch. 3.2 - Prob. 39E Ch. 3.2 - Prob. 40E Ch. 3.2 - Prob. 41E Ch. 3.3 - YOUR TURN 1 The projected U.S. Asian population...Ch. 3.3 - Prob. 2YT Ch. 3.3 - Prob. 3YT Ch. 3.3 - Prob. 4YT Ch. 3.3 - Prob. 5YT Ch. 3.3 - Prob. 1WE Ch. 3.3 - Prob. 2WE Ch. 3.3 - Prob. 3WE Ch. 3.3 - Prob. 4WE Ch. 3.3 - Prob. 1E Ch. 3.3 - Find the average rate of change for each function...Ch. 3.3 - Prob. 3E Ch. 3.3 - Prob. 4E Ch. 3.3 - Find the average rate of change for each function...Ch. 3.3 - Find the average rate of change for each function...Ch. 3.3 - Find the average rate of change for each function...Ch. 3.3 - Prob. 8E Ch. 3.3 - Prob. 9E Ch. 3.3 - Prob. 10E Ch. 3.3 - Prob. 11E Ch. 3.3 - Prob. 12E Ch. 3.3 - Prob. 13E Ch. 3.3 - Prob. 14E Ch. 3.3 - Find the instantaneous rate of change for each...Ch. 3.3 - Find the instantaneous rate of change for each...Ch. 3.3 - Prob. 17E Ch. 3.3 - Find the instantaneous rate of change for each...Ch. 3.3 - Prob. 19E Ch. 3.3 - Prob. 20E Ch. 3.3 - Prob. 21E Ch. 3.3 - Prob. 22E Ch. 3.3 - Prob. 23E Ch. 3.3 - Prob. 24E Ch. 3.3 - Prob. 25E Ch. 3.3 - 26. Revenue The revenue (in thousands of dollars)...Ch. 3.3 - Prob. 27E Ch. 3.3 - 28. Interest If $1000 is invested in an account...Ch. 3.3 - Prob. 29E Ch. 3.3 - Prob. 30E Ch. 3.3 - Prob. 31E Ch. 3.3 - Prob. 32E Ch. 3.3 - Prob. 33E Ch. 3.3 - Prob. 34E Ch. 3.3 - Prob. 35E Ch. 3.3 - Prob. 36E Ch. 3.3 - Prob. 37E Ch. 3.3 - Prob. 38E Ch. 3.3 - Prob. 39E Ch. 3.3 - Prob. 40E Ch. 3.3 - Prob. 41E Ch. 3.3 - Prob. 42E Ch. 3.3 - Prob. 43E Ch. 3.3 - Prob. 44E Ch. 3.4 - YOUR TURN 1 For the graph of f(x) = x2 − x, (a)...Ch. 3.4 - Prob. 2YT Ch. 3.4 - Prob. 3YT Ch. 3.4 - Prob. 4YT Ch. 3.4 - Prob. 5YT Ch. 3.4 - Prob. 6YT Ch. 3.4 - Prob. 7YT Ch. 3.4 - Find for each of the following...Ch. 3.4 - Prob. 2WE Ch. 3.4 - Prob. 3WE Ch. 3.4 - Prob. 4WE Ch. 3.4 - 1. By considering, but not calculating, the slope...Ch. 3.4 - Prob. 2E Ch. 3.4 - Prob. 3E Ch. 3.4 - Prob. 4E Ch. 3.4 - Prob. 5E Ch. 3.4 - Prob. 6E Ch. 3.4 - Prob. 7E Ch. 3.4 - Estimate the slope of the tangent line to each...Ch. 3.4 - Prob. 9E Ch. 3.4 - Prob. 10E Ch. 3.4 - Prob. 11E Ch. 3.4 - Using the definition of the derivative, find...Ch. 3.4 - Prob. 13E Ch. 3.4 - Prob. 14E Ch. 3.4 - Prob. 15E Ch. 3.4 - Prob. 16E Ch. 3.4 - Using the definition of the derivative, find...Ch. 3.4 - Using the definition of the derivative, find...Ch. 3.4 - Prob. 19E Ch. 3.4 - Using the definition of the derivative, find...Ch. 3.4 - Prob. 21E Ch. 3.4 - For each function, find (a) the equation of the...Ch. 3.4 - For each function, find (a) the equation of the...Ch. 3.4 - For each function, find (a) the equation of the...Ch. 3.4 - For each function, find (a) the equation of the...Ch. 3.4 - For each function, find (a) the equation of the...Ch. 3.4 - Prob. 27E Ch. 3.4 - Prob. 28E Ch. 3.4 - Prob. 29E Ch. 3.4 - Prob. 30E Ch. 3.4 - Prob. 31E Ch. 3.4 - Prob. 32E Ch. 3.4 - Prob. 33E Ch. 3.4 - Prob. 34E Ch. 3.4 - Find the x-values where the following do not have...Ch. 3.4 - Find the x-values where the following do not have...Ch. 3.4 - Prob. 37E Ch. 3.4 - Find the x-values where the following do not have...Ch. 3.4 - Prob. 39E Ch. 3.4 - In Exercises 40 and 41, tell which graph, (a) or...Ch. 3.4 - Prob. 41E Ch. 3.4 - Prob. 42E Ch. 3.4 - Prob. 43E Ch. 3.4 - Prob. 44E Ch. 3.4 - Prob. 45E Ch. 3.4 - Prob. 46E Ch. 3.4 - Prob. 47E Ch. 3.4 - Prob. 48E Ch. 3.4 - 49. Demand Suppose the demand for a certain item...Ch. 3.4 - Prob. 50E Ch. 3.4 - Prob. 51E Ch. 3.4 - 52. Cost The cost in dollars of producing x tacos...Ch. 3.4 - Prob. 54E Ch. 3.4 - Prob. 55E Ch. 3.4 - Prob. 56E Ch. 3.4 - Prob. 57E Ch. 3.4 - Prob. 58E Ch. 3.4 - Prob. 59E Ch. 3.4 - Prob. 60E Ch. 3.4 - Prob. 61E Ch. 3.5 - YOUR TURN 1 Sketch the graph of the derivative of...Ch. 3.5 - Prob. 2YT Ch. 3.5 - Prob. 1WE Ch. 3.5 - Prob. 2WE Ch. 3.5 - Prob. 1E Ch. 3.5 - Prob. 2E Ch. 3.5 - Prob. 3E Ch. 3.5 - Prob. 4E Ch. 3.5 - Prob. 5E Ch. 3.5 - Prob. 6E Ch. 3.5 - Prob. 7E Ch. 3.5 - Sketch the graph of the derivative for each...Ch. 3.5 - Sketch the graph of the derivative for each...Ch. 3.5 - Prob. 10E Ch. 3.5 - Prob. 11E Ch. 3.5 - Sketch the graph of the derivative for each...Ch. 3.5 - Prob. 13E Ch. 3.5 - Prob. 14E Ch. 3.5 - Prob. 15E Ch. 3.5 - Prob. 16E Ch. 3.5 - Business and Economics 17. Consumer Demand When...Ch. 3.5 - Prob. 18E Ch. 3.5 - Prob. 19E Ch. 3.5 - 20. Flight Speed The graph below shows the...Ch. 3.5 - Prob. 21E Ch. 3.5 - 22. Weight Gain The graph below shows the typical...Ch. 3.5 - Prob. 23E Ch. 3.5 - Prob. 24E Ch. 3 - Prob. 1RE Ch. 3 - Prob. 2RE Ch. 3 - Prob. 3RE Ch. 3 - Prob. 4RE Ch. 3 - Determine whether each of the following statements...Ch. 3 - Prob. 6RE Ch. 3 - Prob. 7RE Ch. 3 - Prob. 8RE Ch. 3 - Prob. 9RE Ch. 3 - Prob. 10RE Ch. 3 - Prob. 11RE Ch. 3 - Prob. 12RE Ch. 3 - Prob. 13RE Ch. 3 - Prob. 14RE Ch. 3 - Prob. 15RE Ch. 3 - Prob. 16RE Ch. 3 - Prob. 17RE Ch. 3 - Prob. 18RE Ch. 3 - Prob. 19RE Ch. 3 - Prob. 20RE Ch. 3 - Prob. 21RE Ch. 3 - Prob. 22RE Ch. 3 - Prob. 23RE Ch. 3 - Prob. 24RE Ch. 3 - Prob. 25RE Ch. 3 - Prob. 26RE Ch. 3 - Prob. 27RE Ch. 3 - Prob. 28RE Ch. 3 - Prob. 29RE Ch. 3 - Prob. 30RE Ch. 3 - Prob. 31RE Ch. 3 - Prob. 32RE Ch. 3 - Prob. 33RE Ch. 3 - Prob. 34RE Ch. 3 - Prob. 35RE Ch. 3 - Prob. 36RE Ch. 3 - Prob. 37RE Ch. 3 - Prob. 38RE Ch. 3 - Prob. 39RE Ch. 3 - Prob. 40RE Ch. 3 - Prob. 41RE Ch. 3 - Prob. 42RE Ch. 3 - Prob. 43RE Ch. 3 - Prob. 44RE Ch. 3 - Prob. 45RE Ch. 3 - Prob. 46RE Ch. 3 - Prob. 47RE Ch. 3 - Prob. 48RE Ch. 3 - Prob. 49RE Ch. 3 - Prob. 50RE Ch. 3 - Prob. 51RE Ch. 3 - Prob. 52RE Ch. 3 - Prob. 53RE Ch. 3 - Prob. 54RE Ch. 3 - Prob. 55RE Ch. 3 - Prob. 56RE Ch. 3 - Prob. 57RE Ch. 3 - Prob. 58RE Ch. 3 - Prob. 59RE Ch. 3 - Prob. 60RE Ch. 3 - Prob. 61RE Ch. 3 - Prob. 62RE Ch. 3 - Prob. 63RE Ch. 3 - Prob. 64RE Ch. 3 - Prob. 65RE Ch. 3 - Prob. 66RE Ch. 3 - Prob. 67RE Ch. 3 - Prob. 68RE Ch. 3 - Prob. 69RE Ch. 3 - Prob. 70RE Ch. 3 - Prob. 71RE Ch. 3 - Prob. 72RE Ch. 3 - Prob. 73RE

Knowledge Booster

$Calculus$

Learn more about

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