Consider the piecewise defined function w(t) modeling the rate at which sand enters a container, and the differentiable function G(t) modeling the rate at which sand leaves the container. Both...

Calculus BC piecewise function

Extracted text: Consider the piecewise defined function w(t) modeling the rate at which sand enters a container, and the differentiable function G(t) modeling the rate at which sand leaves the container. Both functions are measured in L/hr and at t = 1 hour there are 500 L in the container. I> 2 3cos( 51 – 10) + 13, 0<><2 |1="" 4="" 9="" 12="" g),="" l/hr="" 10="" 8="" 15="" 22="" t="" 61="" +="" 4,="" w(="" t)="a)" is="" w(t)="" continuous="" at="" t="2?" is="" w(t)="" differentiable="" at="" t="2?" justify="" your="" answer.="" b)="" use="" a="" right="" riemann="" sum="" with="" two="" subintervals="" indicated="" by="" the="" chart="" to="" approximate="" the="" amount="" of="" sand="" that="" has="" exited="" the="" container="" on="" 1sts="" 9.="" show="" your="" process.="" c)="" is="" the="" amount="" of="" sand="" in="" the="" tank="" increasing="" or="" decreasing="" at="" t="4." give="" a="" reason="" for="" your="" answer.="" d)="" using="" mean="" value="" theorem="" yields="" the="" approximation="" for="" g'(2.5)="" .="" using="" correct="" units,="" explain="" the="" meaning="" of="" this="" value="" in="" the="" context="" of="" the="" question.="" 3="" e)="" evaluate="" í="" w(t)dt.="" show="" your="" process.="" (remember="" don't="" simplify)="" 1="" f)="" write="" an="" equation="" that="" would="" represent="" the="" time="" k="" when="" the="" container="" has="" 545="" l="" of="" sand="" in="" it.="" do="" not="" solve.="" g)="" consider="" the="" function="" given="" by="" h'(t)="w(t)" +="" g(t)="" and="" give="" the="" second="" degree="" taylor="" polynomial="" centered="" at="" t="4" for="" h(t).="" it="" is="" known="" that="" h(4)="20" and="" g'(4)="-9." h)="" write="" an="" expression="" for="" the="" length="" of="" w(t)="" from="" t="0" to="" t="2." do="" not="" solve.="" i)="" find="" an="" antiderivative="" that="" could="" be="" used="" to="" evaluate="" į="" t="" -="" g"(t)dt.="">