Calculus: Graphical, Numerical, Algebraic

3rd Edition

ISBN: 9780133688399

Author: Finney, Ross L.

Publisher: Pearson/Prentice Hall

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…

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Question

Chapter 2.1, Problem 34E

To determine

To find: The value of limx→5(x3−125x−5) with the help of graph and check the results algebraically.

Expert Solution & Answer

Answer to Problem 34E

The value of limx→5(x3−125x−5) is 75 .

Explanation of Solution

Given information: The limit is limx→5(x3−125x−5) .

Calculation:

Let y=x3−125x−5 to find the value of limx→5(x3−125x−5) graphically.

To graph a function y=x3−125x−5 , follow the steps using graphing calculator.

First press “ON” button on graphical calculator, press Y= key and enter right hand side of the equation y=x3−125x−5 after the symbol Y1 . Enter the keystrokes (X^3−125)÷(X−5) .

The display will show the equation,

Y1=(X^3−125)/(X−5)

Now, press the GRAPH key and TRACE key to produce the graph of given function in standard window as shown below.

Calculus: Graphical, Numerical, Algebraic, Chapter 2.1, Problem 34E

Figure (1)

The function x3−125x−5 tends to 75 as x tends to 5 from both the sides. So, the value of limx→5(x3−125x−5) graphically is 75 .

Check the limit algebraically.

limx→5(x3−125x−5)=limx→5(x3−53x−5)=limx→5((x−5)(x2+5x+52)x−5)=limx→5(x2+5x+52)=52+5×5+52

Further simplify.

limx→5(x3−125x−5)=25+25+25=75

So, the value of limx→5(x3−125x−5) is equal to 75 .

Therefore, the value of limx→5(x3−125x−5) is 75 .

Chapter 2.1, Problem 33E

Chapter 2.1, Problem 35E

Chapter 2 Solutions

Calculus: Graphical, Numerical, Algebraic

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The value of lim x → 5 ( x 3 − 125 x − 5 ) with the help of graph and check the results algebraically.