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what is the limit of comparison test for improper integrals?

Short Answer

Expert verified

if f and g are continuous ,positive functions for all values of x and .

then 1) if 0<k<then ag(x)dxconverges then af(x)dxconverges.

2) if k=0 then ag(x)dxconverges thenaf(x)dxconverges.

3) if k=then ag(x)dxconverge thenaf(x)dxconverges.

Step by step solution

01

the limit of comparison test for improper integrals

if f and g are continuous ,positive functions for all values of x and limxf(x)g(x)=k.

then 1) if localid="1651481834930" 0<k<then localid="1651481820957" ag(x)dxconverges thenlocalid="1651481826895" af(x)dxconverges.

2) if k=0 then ag(x)dxconverges thenaf(x)dxconverges.

3) if k=thenag(x)dxconverge thenaf(x)dxconverges.

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