9. Sequence and Series - 9 Sequences and Series Improper Integrals(Cont and Disc ∞ b � f(x dx = lim ● If ​f ​ is continuous on[a ∞ then

9. Sequence and Series - 9 Sequences and Series...

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9. Sequences and Series Improper Integrals(Cont and Disc) If f is continuous on a,),then(x) dx(x) dxaf=limb→ ∞ bafIf f is continuous on −,],then(x) dx(x) dx(a−∞f=limb→ −∞ bafIf f is continuous on −,),then(x) dx(x) dx(x) dx,cε R(−∞f= c−∞f+cfDiscontinuities May Occur 1.If fis continuous on a,),then(x) dx(x) dx[baf=limcbcaf2.If fis continuous on a,],then(x) dx(x) dx(baf=limca+bcf3.f fis continuous on a, ) u(c,],then(x) dx(x) dx(x) dx[baf=caf+bcfEx:Determine if the integralisdx0−∞13−xconvergent or divergent 1.Find the limit of the integral dxlimb→ −∞ [ a ∞ ∞ b b c b 2.Determine whether integral converges or diverges . The nrepresentes Keep in mind that a sequence is a listing of terms. Let’s see an example of writing the formula of a sequence: Ex:5, 8, 11, 14, 17. What is the formula for the sequence? 1.Check to see a pattern between each term
lim 1

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