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3. Let<br>(0 <x < 1)<br>f(x) =<br>2x;<br>(1< x < 2)<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(x) =<br>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 r = 1?<br>

Extracted text: 3. Let (0 < 1)="" f(x)="2x;">< x="">< 2)="" i)="" is="" the="" function="" f(x)="" continuous="" on="" [0,="" 2]?="" explain="" (a="" graph="" is="" not="" a="" proof!)="" ii)="" compute="" and="" graph="" the="" function="" f(x)="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="" r="">

Jun 05, 2022

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