6"! I a You must show all your work to get full marks. | . Determine lim f(.-r) and lim 3"(1) for the function. Clearly state the conditions you use. 3*" I-F-M Then. give the horizontal asymptotes of j (if any). 33:" + 2 3qu + 10 a. 1' = l). I = M ) 21:3 + We + 1 H ) e' . If a function f represents a system that varies in time. the existence of lim f (t) means that the system l-rno reaches a steady state (or equilibrium). For the following system, determine if a steady state exists and give the steady-state value. The amount of drug {in milligrams) in the blood after an IV tube is inserted is given by mu) = 2u0(1 2") . Let J's-41+2 HIS? I(I)={ 23224 ifr>2. a. Use the continuity checklist to show that f is not continuous at r = 2. b. Determine whether I is continuous from the left or the right at :l'.' = 2. c. St ate the interval(s) of continuity. . Use the three continuity conditions and determine the value of the constant a for which the function 32+3I1l} MP5 HT): :r+5 a ifs:=5 is continuous at 5. . Let {_)_ 1 ifaczfl 9" 1 sun. W'rite a formula for |g(r)|. Is 9 continuous at I = 0'? Explain. Is |g| continuous at :c = (1? Explain. 9??? For any function f, if |f| is continuous at a. does it necessarin follow that f is continuous at 0.? Explain