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A: ,

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A: Let f(x)=x3-x-1Here x3-x-1=0∴x3-x=1∴x(x2-1)=1∴x=1(x2-1)∴ϕ(x)=1(x2-1)Here f(1)=-1<0 and…

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Q: 9. Determine by the root test if Ln=2 (4n-5\n 2n+1, converges or diverges.

A: Explained below

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A: ANSWER :

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A: Now we will solve the problem.

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Q: 2an-butn Converge bey to

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Q: 7). but you have not said if the diverges test applies or not . please xeplain the final solution ?

A: This question can be solved using the concept of divergence test.

Q: sech2(In x)

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A: Given fx=x3+x-4 xx2+1=4x=4x2+1ϕ(x)=4x2+1 f1=13+1-4=-2<-0 and f2=23+2-4=6>0 thus the roots lies…