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02.28.08_Page_2 - Divergent so ELIdx diverges x lim mi ml H...

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Unformatted text preview: Divergent so ELIdx diverges! x _ lim mi ml H If we didn’t notice that the above integral is improper then 3 0 ildx=1n|x—1lj=1n2—1n1=1n2 Which is WRONG x- What type of integral is this? TypeI Ime'xdx=lim te'xdx=lim —e-x l;]=1im l—e't]=1 0 fans 0 tam tam oo 2 0 2 DD 2 I xe'x dx 2] xe'x dx+I xe'”C dxz no em 0 = lim [L0 xe'xza'x] + lim (:[xe'xzdx] raise tam = lim [—le'xz S]+ lim [—le'xz g] faim 2 tam 2 . 1 l 42 . 1 42 1 =11m ——+—e +11m ——e +— t—>—w 2 2 t—wo 2 2 Comparison Theorem Suppose f and g are continuous functions with f (x) 2 g(x) Z 0 for x 2 a a) If I50 f (x)dx is convergent then Img(x)dx is convergent b) If Ibo g(x)dx is divergent; then r f (3005K is also divergent Diagram 4 —dx—? ml 3 ‘1 J-l +xe ...
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