   Chapter 9.1, Problem 41E Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Solutions

Chapter
Section Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

In Problems 41-44, graph each function with a graphing calculator and use it to predict the limit. Check your work either by using the table feature of the calculator or by finding the limit algebraically. lim x → 10 x 2 − 19 x + 90 3 x 2 − 30 x

To determine

To calculate: The function f(x)=x219x+903x230x using a graphing calculator, and predict the limit, limx10x219x+903x230x Also, check the limit.

Explanation

Given Information:

The function is f(x)=x219x+903x230x.

The limit is limx10x219x+903x230x.

Calculation:

Consider the provided limit,

limx10x219x+903x230x

The limit from the left is represented by limx10f(x) and the limit from the right is represented by limx10+f(x).

The limxcf(x) will exist at c=10 when the limit from the left, that is, the values of f(c) but c<10, is equal to the limit from the right, that is, the values of f(c) but c>10.

limx10f(x)=0.033

And,

limx10f(x)=0.033

Since,

limx10f(x)=limx10+f(x)

Hence, the value of limx10x219x+903x230x is 0.033.

To check the value of the limit, solve for the value of the limit.

Consider the provided limit,

limx10x219x+903x230x

Solve it by substituting 10 for x,

limx10x219x+903x230x=(10)219(10)+903(10)230(10)=100190+903(100)300=100190+90300300=00

Since, the limit has 00 indeterminate form at x=10

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