Chapter 9.1, Problem 41E

### Mathematical Applications for the ...

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

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)=x2âˆ’19x+903x2âˆ’30x.

The limit is limxâ†’10x2âˆ’19x+903x2âˆ’30x.

Calculation:

Consider the provided limit,

limxâ†’10x2âˆ’19x+903x2âˆ’30x

The limit from the left is represented by limxâ†’10âˆ’f(x) and the limit from the right is represented by limxâ†’10+f(x).

The limxâ†’cf(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.

limxâ†’10âˆ’f(x)=0.033

And,

limxâ†’10âˆ’f(x)=0.033

Since,

limxâ†’10âˆ’f(x)=limxâ†’10+f(x)

Hence, the value of limxâ†’10x2âˆ’19x+903x2âˆ’30x is 0.033.

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

Consider the provided limit,

limxâ†’10x2âˆ’19x+903x2âˆ’30x

Solve it by substituting 10 for x,

limxâ†’10x2âˆ’19x+903x2âˆ’30x=(10)2âˆ’19(10)+903(10)2âˆ’30(10)=100âˆ’190+903(100)âˆ’300=100âˆ’190+90300âˆ’300=00

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

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