Question

officials in a certain region tend to raise the sales tax in years in which the state faces a budget deficit and then cut the tax when the state has a surplus. the graph shows the regions sales tax in recent years. let ( t(x) ) represent the sales tax per dollar spent in year ( x ). find the desired limits and values, if they exist. note that 01 represents 2001. complete parts (a) through (e). (a) find ( lim_{x
ightarrow2009}t(x) ). select the correct choice below and, if necessary, fill in the answer box within your choice. ( \bigcirc ) a. ( lim_{x
ightarrow2009}t(x)=square ) cent(s) (type an integer or a decimal.) ( \bigcirc ) b. the limit does not exist and is neither ( infty ) nor ( -infty ).

Explanation:

Step1: Recall the definition of the limit

The limit of a function \(T(x)\) as \(x\to a\) is the value that \(T(x)\) approaches as \(x\) gets arbitrarily close to \(a\) (from both sides).

Step2: Analyze the graph near \(x = 2009\)

Looking at the graph, as \(x\) approaches \(2009\), the value of \(T(x)\) approaches \(7.5\) cents.

Answer:

A. \(\lim_{x\to2009}T(x)=7.5\) cent(s)