12.9 The Limit-Comparison Test for improper integrals

[@vixguy]

Why does f and g both need to be positive? The theorem works fine in any case, no?

[@SethKadam-j7v]

3:30 I wish you would have explained this step more thoroughly, it was difficult to understand how you got one, and the L-hopitals rule took quite some time.

[@kaanalpkozanl3914]

You saved my day with this video, awesome sir!

[@CRAZYMUSIC80]

Kaan Alp Kozanlı calculus finalin var dimi :)

[@yusuf_kizilkaya]

@@CRAZYMUSIC80 hepimizin var :]

[@mikerainam6943]

Simple short and a good one.. Thank you

[@ethanyoung1894]

This really helped, I appreciate it!!!!

[@razorblake393]

How do u determine g(x)

[@vaderanomaly1573]

Would help if you actually showed steps in solving the limits, i have no idea how it's 1

[@ozackerman7665]

I guess you can just use L'Hopital's Rule since the limit as x approaches 0 of sinx/x = 0/0.

[@dmusical7527]

Awesome explaination sir

[@ujjwal2473]

Helped a lot. Thanks :)

[@slagunes9751]

Is f(x) should be greater than g(x)?

[@kaankosti1279]

what a legend

[@taliakshafir]

For example 1, when I computed the limit as x approaches infinity of f(x)/g(x), the answer I got was infinity. How do I get 1 as my answer? Thanks.

[@mat1378]

Reduce to a single fraction, then factor the biggest term from both numerator and denominator. It is x^(5/2) in both cases.

[@oemr2121]

thank you so much sir

[@kelvinkayuni8331]

thank's a lot sir, but I'm confused here, is 0/0 equal to 1 or infinity?, why is that limit of sin(1/x2)/(1/x2) comes to 1 but not infinity, though we get 0/0 ?

[@Shivangrana532]

Thank you

[@najeebullah-yw3hv]

limit x approching to infinity (sin1/x^2÷1/x^2 = 0 not 1

[@mat1378]

The limit as x approaches infinity is 1. The limit as x approaches 0 is 0.

[@MegaMsc123]

Ok this is epic

[@DAT-OFFICIAL]

If young Black Panther was to give math lessons:

[@najeebullah-yw3hv]

by squeez theorem

[@mat1378]

Use Squeeze Theorem carefully. As x approaches infinity, the limit of 1/(1/x^2) is infinity, not 0, because 1/(1/x^2))=x^2. Squeeze Theorem does not draw any conclusion in this case.

[@najeebullah-yw3hv]

MAT137 so why is this confusion

[@eleonorroncalez7025]

I am confuse right now, i thought if we get a value it is convergent 🥺

[@minkihairoil]

It is! He made a mistake there. Divergent is when you get +/-infty or it DNE; convergent is when you get a number!