3. Let (0


Just the last two parts. Thanks. (iii, iv).


3. Let<br>(0 <x < 1)<br>(1 < x < 2)<br>f(x) =<br>2x;<br>i) Is the function f(x) continuous on [0, 2]? Explain (a graph is not a proof!)<br>ii) Compute AND graph the function<br>F(æ) = | f(t)dt<br>Hint: Imitate the proof of the problem in the notes/video about the relatioship between<br>integration and differentiation.<br>ii) Is the function F(x) continuous at x = 1?<br>iii) Does F'(1) exist? Explain. (Hint: Compute the derivative of F(x) from the left and<br>right at x = 1<br>iv) Does iii) violate the FTC II that states F'(x) = f(x) for all x at which f is continuous?<br>

Extracted text: 3. Let (0 < 1)="" (1="">< x="">< 2)="" f(x)="2x;" i)="" is="" the="" function="" f(x)="" continuous="" on="" [0,="" 2]?="" explain="" (a="" graph="" is="" not="" a="" proof!)="" ii)="" compute="" and="" graph="" the="" function="" f(æ)="|" f(t)dt="" hint:="" imitate="" the="" proof="" of="" the="" problem="" in="" the="" notes/video="" about="" the="" relatioship="" between="" integration="" and="" differentiation.="" ii)="" is="" the="" function="" f(x)="" continuous="" at="" x="1?" iii)="" does="" f'(1)="" exist?="" explain.="" (hint:="" compute="" the="" derivative="" of="" f(x)="" from="" the="" left="" and="" right="" at="" x="1" iv)="" does="" iii)="" violate="" the="" ftc="" ii="" that="" states="" f'(x)="f(x)" for="" all="" x="" at="" which="" f="" is="">

Jun 05, 2022
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