Chapter 9.1, Problem 65E

### 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

# Federal income tax The following table shows part of a tax rate schedule for single filers. Use this schedule and create a table of values that could be used to find the following limits, if they exist. Let x represent the amount of taxable income and let T(x) represent the tax due.(a) lim x → 36 , 900 − T ( x ) (b) lim x → 36 , 900 + T ( x ) (c) lim x → 36 , 900 T ( x ) Single Filers If taxable income is over— But notover— The tax is: $0$9075 10 % of the amount over $0$9075 $36,900$907.50 plus 15 % of the amount over 9075 $36,900$89,350 $5081.25 plus 25 % of the amount over 36,900$89,350 $186,350$18,193.75 plus 28 % of the amount over 89,350 Source: Internal Revenue Service

(a)

To determine

To calculate: The value of the limit limx36,900T(x) by the use of a table that could be created by the provided table below.

 Single Filers If taxable income is over But not over The tax is $0$9075 10% of the amount over $0$9075 $36,900$907.50 plus 15% of the amount over 9075 $36,900$89,350 $5081.25 plus 25% of the amount over 36,900$89,350 $186,350$18,193.75 plus 28% of the amount over 89,350
Explanation

Given information:

The provided limit is limx36,900T(x), x denotes the amount of taxable income and T(x) denotes the due tax. The provided table is below.

 Single Filers If taxable income is over But not over The tax is $0$9075 10% of the amount over $0$9075 $36,900$907.50 plus 15% of the amount over 9075 $36,900$89,350 $5081.25 plus 25% of the amount over 36,900$89,350 $186,350$18,193.75 plus 28% of the amount over 89,350

Formula used:

For a polynomial function f(x)=anxn+an1xn1++a1x+a0 where an0 and n is a positive integer,

limxcf(x)=f(c)

This is defined for all values of c.

Calculation:

Consider the provided limit,

limx36,900T(x)

Now consider the provided table and x denotes the amount of taxable income and T(x) denotes the due tax.

To find the limit of limx36,900T(x), first create a table by the use of provided table as.

 Single Filers If taxable income is over But not over Due tax $0$9075 10%x $9075$36,900 $907.50+15%(x−9075)$36,900 $89,350$5081

(b)

To determine

To calculate: The value of the limit limx36,900+T(x) by the use of a table that could be created by the provided table below.

 Single Filers If taxable income is over But not over The tax is $0$9075 10% of the amount over $0$9075 $36,900$907.50 plus 15% of the amount over 9075 $36,900$89,350 $5081.25 plus 25% of the amount over 36,900$89,350 $186,350$18,193.75 plus 28% of the amount over 89,350

(c)

To determine

To calculate: The value of the limit limx36,900T(x) by the use of a table that could be created by the provided table below.

 Single Filers If taxable income is over But not over The tax is $0$9075 10% of the amount over $0$9075 $36,900$907.50 plus 15% of the amount over 9075 $36,900$89,350 $5081.25 plus 25% of the amount over 36,900$89,350 $186,350$18,193.75 plus 28% of the amount over 89,350

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