Chapter 9.1, Problem 63E

Federal income tax The following table shows part of the April 15, 2015, 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 $T\left(x\right)$ represent the tax due.

(a) $\underset{x\to 36,{900}^{-}}{\lim }T(x)$

(b) $\underset{x\to 36,{900}^{+}}{\lim }T(x)$

(c) $\underset{x\to 36,900}{\lim }T(x)$

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

Source: Internal Revenue Service