Chapter 11.9, Problem 29E

Work these exercises. (See Examples 3 and 4.)

State Sales Tax Officials in California have raised and lowered the state sales tax in various years, as shown in the accompanying figure. Let $T\left(x\right)$ represent the sales tax rate (as a percentage) in year x Find the given quantities. (Data from: www.boe.ca.govlsutaxltaxrateshist.htm.)

$\text{limx}\to \text{2010-T}\left(\text{x}\right)$

$\text{limx}\to \text{2010+T}\left(\text{x}\right)$

$\text{limx}\to \text{2010T}\left(\text{x}\right)$

$\text{limx}\to \text{2017-T}\left(\text{x}\right)$

$\text{limx}\to \text{2017+T}\left(\text{x}\right)$

$\text{limx}\to \text{2017T}\left(\text{x}\right)$

Find all values on the interval (2001, 2018) where T is discontinuous.

Find all values on the interval (2001, 2018) where T is not differentiable.