(a) Explanation Calculation: Given function is, lim x → 1 x 4 + 2 x 3 + 2 x 2 − 10 x + 5 x 2 − 1 . As x approaches 1, the denominator value becomes zero. Then the value of the function is undefined. So, substitute the values for x which is nearer to 1 from the right and left. Substitute x = 1.1 in the difference quotient and compute the value of the given function as follows. x 4 + 2 x 3 + 2 x 2 − 10 x + 5 x 2 − 1 = ( 1.1 ) 4 + 2 ( 1.1 ) 3 + 2 ( 1.1 ) 2 − 10 ( 1.1 ) + 5 ( 1.1 ) 2 − 1 = 1.4641 + 2 ( 1.331 ) + 2 ( 1.21 ) − 11 + 5 1.21 − 1 = 1.4641 + 2.662 + 2.42 − 11 + 5 0.21 = 0.5461 0.21 ≈ 2.6005 Substitute x = 1.01 in the difference quotient and compute the value of the given function as follows. x 4 + 2 x 3 + 2 x 2 − 10 x + 5 x 2 − 1 = ( 1.01 ) 4 + 2 ( 1.01 ) 3 + 2 ( 1.01 ) 2 − 10 ( 1.01 ) + 5 ( 1.01 ) 2 − 1 = 1.04060401 + 2 ( 1.030301 ) + 2 ( 1.0201 ) − 10.1 + 5 1.0201 − 1 = 1.04060401 + 2.060602 + 2.0402 − 10.1 + 5 0.0201 = 0.04140601 0.0201 ≈ 2.0600 Substitute x = 1.001 in the difference quotient and compute the value of the given function as follows. x 4 + 2 x 3 + 2 x 2 − 10 x + 5 x 2 − 1 = ( 1.001 ) 4 + 2 ( 1.001 ) 3 + 2 ( 1.001 ) 2 − 10 ( 1.001 ) + 5 ( 1.001 ) 2 − 1 = 1.004006004 + 2 ( 1.003003001 ) + 2 ( 1.002001 ) − 10.01 + 5 1.002001 − 1 = 1.004006004 + 2.006006002 + 2.004002 − 10.01 + 5 0.002001 = 0.04140601 0.002001 ≈ 2.006 Thus, if x approaches 1 from the right, then f ( x ) value is 2. Substitute x = 0.99 in the difference quotient and compute the value of the given function as follows (b) To determine To sketch: The given function using graphing calculator.

Finite Mathematics and Calculus with Applications Books a la Carte Plus MyLab Math Package (10th Edition)

10th Edition

ISBN: 9780133935592

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 11, Problem 45RE

(a)

To determine

To find: The value of the given function near the point x=1 .

(b)

To determine

To sketch: The given function using graphing calculator.

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Chapter 11, Problem 44RE

Chapter 11, Problem 46RE

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Consider the function f(x) = x²-1. (a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative. Show all your steps clearly. (b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the graph where x 1 and x-> 1+h (for a small positive value of h, illustrate conceptually). Then, draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the value you found in part (a). (c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in the context of the graph of f(x). How does the rate of change of this function vary at different points?

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Chapter 11 Solutions

Finite Mathematics and Calculus with Applications Books a la Carte Plus MyLab Math Package (10th Edition)

Ch. 11.1 - Find limx1(x2+2).Ch. 11.1 - Find limx2x24x2.Ch. 11.1 - Prob. 3YT Ch. 11.1 - Prob. 4YT Ch. 11.1 - Prob. 5YT Ch. 11.1 - Prob. 6YT Ch. 11.1 - Prob. 7YT Ch. 11.1 - Prob. 8YT Ch. 11.1 - Prob. 1WE Ch. 11.1 - Prob. 2WE

Ch. 11.1 - Prob. 3WE Ch. 11.1 - Prob. 4WE Ch. 11.1 - In Exercises 1-4, choose the best answer for each...Ch. 11.1 - In Exercises 1-4, choose the best answer for each...Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E Ch. 11.1 - Prob. 11E Ch. 11.1 - Prob. 12E Ch. 11.1 - Prob. 13E Ch. 11.1 - Prob. 14E Ch. 11.1 - Prob. 15E Ch. 11.1 - Prob. 16E Ch. 11.1 - Prob. 17E Ch. 11.1 - Prob. 18E Ch. 11.1 - Complete the tables and use the results to find...Ch. 11.1 - Prob. 20E Ch. 11.1 - Prob. 21E Ch. 11.1 - Prob. 22E Ch. 11.1 - Prob. 23E Ch. 11.1 - Prob. 24E Ch. 11.1 - Prob. 25E Ch. 11.1 - Prob. 26E Ch. 11.1 - Prob. 27E Ch. 11.1 - Prob. 28E Ch. 11.1 - Prob. 29E Ch. 11.1 - Prob. 30E Ch. 11.1 - Prob. 31E Ch. 11.1 - Prob. 32E Ch. 11.1 - Prob. 33E Ch. 11.1 - Prob. 34E Ch. 11.1 - Prob. 35E Ch. 11.1 - Prob. 36E Ch. 11.1 - Prob. 37E Ch. 11.1 - Prob. 38E Ch. 11.1 - Prob. 39E Ch. 11.1 - Prob. 40E Ch. 11.1 - Prob. 41E Ch. 11.1 - Prob. 42E Ch. 11.1 - Prob. 43E Ch. 11.1 - Prob. 44E Ch. 11.1 - Prob. 45E Ch. 11.1 - Prob. 46E Ch. 11.1 - Prob. 47E Ch. 11.1 - Prob. 48E Ch. 11.1 - Prob. 49E Ch. 11.1 - Prob. 50E Ch. 11.1 - Prob. 51E Ch. 11.1 - Prob. 52E Ch. 11.1 - Prob. 53E Ch. 11.1 - Prob. 54E Ch. 11.1 - Prob. 55E Ch. 11.1 - Prob. 56E Ch. 11.1 - Does a value of k exist such that the following...Ch. 11.1 - Prob. 58E Ch. 11.1 - Prob. 59E Ch. 11.1 - Prob. 60E Ch. 11.1 - Prob. 61E Ch. 11.1 - Prob. 62E Ch. 11.1 - Prob. 63E Ch. 11.1 - Let G(x)=6(x4)2. (a) Find limx4G(x). (b) Find the...Ch. 11.1 - Prob. 65E Ch. 11.1 - Prob. 66E Ch. 11.1 - Prob. 67E Ch. 11.1 - Prob. 68E Ch. 11.1 - Prob. 69E Ch. 11.1 - Use a graphing calculator to answer the following...Ch. 11.1 - Prob. 71E Ch. 11.1 - Prob. 72E Ch. 11.1 - Prob. 73E Ch. 11.1 - Prob. 74E Ch. 11.1 - Find each of the following limits (a) by...Ch. 11.1 - Find each of the following limits (a) by...Ch. 11.1 - Prob. 77E Ch. 11.1 - Prob. 78E Ch. 11.1 - Prob. 79E Ch. 11.1 - Prob. 80E Ch. 11.1 - Prob. 81E Ch. 11.1 - Prob. 82E Ch. 11.1 - Prob. 83E Ch. 11.1 - Prob. 84E Ch. 11.1 - Sales Tax Officials in California tend to raise...Ch. 11.1 - Prob. 86E Ch. 11.1 - Prob. 87E Ch. 11.1 - Prob. 88E Ch. 11.1 - Prob. 89E Ch. 11.1 - Prob. 90E Ch. 11.1 - Prob. 91E Ch. 11.1 - Prob. 92E Ch. 11.1 - Prob. 93E Ch. 11.1 - Prob. 94E Ch. 11.1 - Prob. 95E Ch. 11.2 - Find all values x = a where the function is...Ch. 11.2 - Find all values of x where the piecewise function...Ch. 11.2 - Prob. 1WE Ch. 11.2 - Prob. 2WE Ch. 11.2 - Prob. 3WE Ch. 11.2 - Prob. 4WE Ch. 11.2 - Prob. 5WE Ch. 11.2 - Prob. 1E Ch. 11.2 - Prob. 2E Ch. 11.2 - Prob. 3E Ch. 11.2 - Prob. 4E Ch. 11.2 - Prob. 5E Ch. 11.2 - Prob. 6E Ch. 11.2 - Prob. 7E Ch. 11.2 - Prob. 8E Ch. 11.2 - Prob. 9E Ch. 11.2 - Prob. 10E Ch. 11.2 - Prob. 11E Ch. 11.2 - Prob. 12E Ch. 11.2 - Prob. 13E Ch. 11.2 - Prob. 14E Ch. 11.2 - Prob. 15E Ch. 11.2 - Prob. 16E Ch. 11.2 - Prob. 17E Ch. 11.2 - Prob. 18E Ch. 11.2 - In Exercises 1924, (a) graph the given function,...Ch. 11.2 - Prob. 20E Ch. 11.2 - Prob. 21E Ch. 11.2 - Prob. 22E Ch. 11.2 - Prob. 23E Ch. 11.2 - Prob. 24E Ch. 11.2 - Prob. 25E Ch. 11.2 - Prob. 26E Ch. 11.2 - Prob. 27E Ch. 11.2 - Prob. 28E Ch. 11.2 - Prob. 29E Ch. 11.2 - Prob. 30E Ch. 11.2 - Prob. 31E Ch. 11.2 - Prob. 32E Ch. 11.2 - Prob. 33E Ch. 11.2 - Prob. 34E Ch. 11.2 - Prob. 35E Ch. 11.2 - Prob. 36E Ch. 11.2 - Prob. 37E Ch. 11.2 - Prob. 38E Ch. 11.2 - Prob. 39E Ch. 11.2 - Prob. 40E Ch. 11.2 - Prob. 41E Ch. 11.3 - Prob. 1YT Ch. 11.3 - Prob. 2YT Ch. 11.3 - Prob. 3YT Ch. 11.3 - Prob. 4YT Ch. 11.3 - Prob. 5YT Ch. 11.3 - Prob. 1WE Ch. 11.3 - Prob. 2WE Ch. 11.3 - Prob. 3WE Ch. 11.3 - Prob. 4WE Ch. 11.3 - Find the average rate of change for each function...Ch. 11.3 - Find the average rate of change for each function...Ch. 11.3 - Find the average rate of change for each function...Ch. 11.3 - Find the average rate of change for each function...Ch. 11.3 - Find the average rate of change for each function...Ch. 11.3 - Find the average rate of change for each function...Ch. 11.3 - Find the average rate of change for each function...Ch. 11.3 - Find the average rate of change for each function...Ch. 11.3 - Suppose the position of an object moving in a...Ch. 11.3 - Suppose the position of an object moving in a...Ch. 11.3 - Suppose the position of an object moving in a...Ch. 11.3 - Suppose the position of an object moving in a...Ch. 11.3 - Suppose the position of an object moving in a...Ch. 11.3 - Suppose the position of an object moving in a...Ch. 11.3 - Find the instantaneous rate of change for each...Ch. 11.3 - Find the instantaneous rate of change for each...Ch. 11.3 - Find the instantaneous rate of change for each...Ch. 11.3 - Find the instantaneous rate of change for each...Ch. 11.3 - Prob. 19E Ch. 11.3 - Prob. 20E Ch. 11.3 - Prob. 21E Ch. 11.3 - Prob. 22E Ch. 11.3 - Prob. 23E Ch. 11.3 - Prob. 24E Ch. 11.3 - ProfitSuppose that the total profit in hundreds of...Ch. 11.3 - Prob. 26E Ch. 11.3 - Prob. 27E Ch. 11.3 - Prob. 28E Ch. 11.3 - Prob. 29E Ch. 11.3 - Prob. 30E Ch. 11.3 - Prob. 31E Ch. 11.3 - Prob. 32E Ch. 11.3 - Prob. 33E Ch. 11.3 - Prob. 34E Ch. 11.3 - Prob. 35E Ch. 11.3 - Prob. 36E Ch. 11.3 - Thermic Effect of FoodThe metabolic rate of a...Ch. 11.3 - Prob. 38E Ch. 11.3 - ImmigrationThe following graph shows how...Ch. 11.3 - Prob. 40E Ch. 11.3 - Prob. 41E Ch. 11.3 - VelocityA car is moving along a straight test...Ch. 11.3 - Prob. 43E Ch. 11.3 - Prob. 44E Ch. 11.4 - Prob. 1YT Ch. 11.4 - Prob. 2YT Ch. 11.4 - Prob. 3YT Ch. 11.4 - Prob. 4YT Ch. 11.4 - Prob. 5YT Ch. 11.4 - If cost is given by C(x) = 10x 0.002x2, find the...Ch. 11.4 - Prob. 7YT Ch. 11.4 - Prob. 1WE Ch. 11.4 - Prob. 2WE Ch. 11.4 - Prob. 3WE Ch. 11.4 - Prob. 4WE Ch. 11.4 - Prob. 1E Ch. 11.4 - (a) Suppose g(x) = x3. Use the graph of g(x) to...Ch. 11.4 - Prob. 3E Ch. 11.4 - Prob. 4E Ch. 11.4 - Prob. 5E Ch. 11.4 - Prob. 6E Ch. 11.4 - Prob. 7E Ch. 11.4 - Prob. 8E Ch. 11.4 - Prob. 9E Ch. 11.4 - Prob. 10E Ch. 11.4 - Prob. 11E Ch. 11.4 - Prob. 12E Ch. 11.4 - Prob. 13E Ch. 11.4 - Prob. 14E Ch. 11.4 - Prob. 15E Ch. 11.4 - Prob. 16E Ch. 11.4 - Prob. 17E Ch. 11.4 - Prob. 18E Ch. 11.4 - Prob. 19E Ch. 11.4 - Prob. 20E Ch. 11.4 - Prob. 21E Ch. 11.4 - Prob. 22E Ch. 11.4 - Prob. 23E Ch. 11.4 - Prob. 24E Ch. 11.4 - For each function, find (a) the equation of the...Ch. 11.4 - Prob. 26E Ch. 11.4 - Prob. 27E Ch. 11.4 - Prob. 28E Ch. 11.4 - Prob. 29E Ch. 11.4 - Prob. 30E Ch. 11.4 - Prob. 31E Ch. 11.4 - Prob. 32E Ch. 11.4 - Prob. 33E Ch. 11.4 - Prob. 34E Ch. 11.4 - Find the x-values where the following do not have...Ch. 11.4 - Prob. 36E Ch. 11.4 - Prob. 37E Ch. 11.4 - Prob. 38E Ch. 11.4 - Prob. 39E Ch. 11.4 - Prob. 40E Ch. 11.4 - Prob. 41E Ch. 11.4 - Prob. 42E Ch. 11.4 - Prob. 43E Ch. 11.4 - Prob. 44E Ch. 11.4 - Prob. 45E Ch. 11.4 - Prob. 46E Ch. 11.4 - Prob. 47E Ch. 11.4 - Prob. 48E Ch. 11.4 - Prob. 49E Ch. 11.4 - Prob. 50E Ch. 11.4 - Prob. 51E Ch. 11.4 - Prob. 52E Ch. 11.4 - Prob. 54E Ch. 11.4 - Prob. 55E Ch. 11.4 - Prob. 56E Ch. 11.4 - Prob. 57E Ch. 11.4 - Prob. 58E Ch. 11.4 - Prob. 59E Ch. 11.4 - Prob. 60E Ch. 11.4 - Prob. 61E Ch. 11.5 - Prob. 1YT Ch. 11.5 - Prob. 2YT Ch. 11.5 - Prob. 1WE Ch. 11.5 - Prob. 2WE Ch. 11.5 - Prob. 1E Ch. 11.5 - Prob. 2E Ch. 11.5 - Prob. 3E Ch. 11.5 - Prob. 4E Ch. 11.5 - Prob. 5E Ch. 11.5 - Prob. 6E Ch. 11.5 - Sketch the graph of the derivative for each...Ch. 11.5 - Prob. 8E Ch. 11.5 - Sketch the graph of the derivative for each...Ch. 11.5 - Sketch the graph of the derivative for each...Ch. 11.5 - Prob. 11E Ch. 11.5 - Prob. 12E Ch. 11.5 - Prob. 13E Ch. 11.5 - Prob. 14E Ch. 11.5 - Prob. 15E Ch. 11.5 - Prob. 16E Ch. 11.5 - Prob. 17E Ch. 11.5 - Prob. 18E Ch. 11.5 - Prob. 19E Ch. 11.5 - Prob. 20E Ch. 11.5 - Prob. 21E Ch. 11.5 - Prob. 22E Ch. 11.5 - Prob. 23E Ch. 11.5 - Prob. 24E Ch. 11 - Determine whether each of the following statements...Ch. 11 - Determine whether each of the following statements...Ch. 11 - Prob. 3RE Ch. 11 - Prob. 4RE Ch. 11 - Prob. 5RE Ch. 11 - Prob. 6RE Ch. 11 - Prob. 7RE Ch. 11 - Prob. 8RE Ch. 11 - Prob. 9RE Ch. 11 - Prob. 10RE Ch. 11 - Prob. 11RE Ch. 11 - Prob. 12RE Ch. 11 - Prob. 13RE Ch. 11 - Prob. 14RE Ch. 11 - Prob. 15RE Ch. 11 - Prob. 16RE Ch. 11 - Prob. 17RE Ch. 11 - Prob. 18RE Ch. 11 - Prob. 19RE Ch. 11 - Prob. 20RE Ch. 11 - Prob. 21RE Ch. 11 - Prob. 22RE Ch. 11 - Prob. 23RE Ch. 11 - Prob. 24RE Ch. 11 - Prob. 25RE Ch. 11 - Prob. 26RE Ch. 11 - Prob. 27RE Ch. 11 - Prob. 28RE Ch. 11 - Prob. 29RE Ch. 11 - Prob. 30RE Ch. 11 - Prob. 31RE Ch. 11 - Prob. 32RE Ch. 11 - Prob. 33RE Ch. 11 - Prob. 34RE Ch. 11 - Prob. 35RE Ch. 11 - Prob. 36RE Ch. 11 - Prob. 37RE Ch. 11 - Prob. 38RE Ch. 11 - Prob. 39RE Ch. 11 - Prob. 40RE Ch. 11 - Prob. 41RE Ch. 11 - Prob. 42RE Ch. 11 - Prob. 43RE Ch. 11 - Prob. 44RE Ch. 11 - Prob. 45RE Ch. 11 - Prob. 46RE Ch. 11 - Find the average rate of change for the following...Ch. 11 - Prob. 48RE Ch. 11 - Prob. 49RE Ch. 11 - Prob. 50RE Ch. 11 - Prob. 51RE Ch. 11 - Prob. 52RE Ch. 11 - Prob. 53RE Ch. 11 - Prob. 54RE Ch. 11 - Prob. 55RE Ch. 11 - Prob. 56RE Ch. 11 - Prob. 57RE Ch. 11 - Prob. 58RE Ch. 11 - Prob. 59RE Ch. 11 - Prob. 60RE Ch. 11 - Prob. 61RE Ch. 11 - Prob. 62RE Ch. 11 - Prob. 63RE Ch. 11 - Marginal AnalysisSuppose the profit (in cents)...Ch. 11 - Prob. 65RE Ch. 11 - Prob. 66RE Ch. 11 - Prob. 67RE Ch. 11 - Prob. 68RE Ch. 11 - Prob. 69RE Ch. 11 - Prob. 70RE Ch. 11 - Prob. 71RE Ch. 11 - Prob. 72RE Ch. 11 - Prob. 73RE

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The value of the given function near the point x = 1 .

Solution Summary: The author explains how to find the value of the given function near the point x=1.