Understand Comparison Theorem For Improper Integral Ex1

comparison theorem, comparison test, improper integral

[@6CornDawg9]

4:11 Thats a big eraser. And thanks, this made understanding converging integrals much easier

[@ralfbodemann1542]

Thanks for the instructive video! In fact, you can use the given convergent integral and the comparison theorem to show that integral C converges. Let I be the integral from 1 to infinity of 1/e^x. I is convergent, therefore k*I is also convergent for any real number k. Now pick k >= e/(e-1) and make the comparison test between k*I and integral C. You will find that x>=1 => k/e^x >= 1/(e^x-1). Thus, integral C converges by the comparison test.

[@gmallick8345]

yeah it's very understandable

[@-a5624]

Thank you so so so much!!

[@-a5624]

This made no sense in my textbook but now it makes perfect sense thank you :)

[@mukeshchand5301]

Why didn't you divide by e to the power x at last in the case of B

[@cassied9327]

To combine the e^x terms at the end of B, you would subtract e^x For example in e^x = b(e^x) you would divide by e^x to solve for b While in e^x = b + e^x you would subtract e^x to solve for b. He doesn’t really “solve for x” because we know x is greater than 0 and e^x plus a number greater than zero is always larger than e^x by itself. I hope I understood the question correctly

[@ayushbudhwani]

Part (A) Can you explain how can x/e^x

[@gamerpedia1535]

We start with that assumption and use proof by contradiction.

[@wristdisabledwriter2893]

The second you went to c I knew the answer was b

[@Santhippe]

Wow such intelligence

[@wristdisabledwriter2893]

@@Santhippe I call it logic.