Been a long time I had my integral class so I forgot almost everything I knew... I need to integrate to see if the serie converge (limn→∞ an = 0). Thus, there is a theorem of the integral, if you evaluate the limit of the integral of a serie when it tends to the infinite minus when x=1 you can determine if the serie is convergent or divergent...(adsbygoogle = window.adsbygoogle || []).push({});

I can`t find a way to start the problems:

1. limt→∞ ∫ [1, t] sin(1/x) dx

2. limt→∞ ∫ [1, t] xe^(-2x) dx

3. limt→∞ ∫ [1, t] 1/(1+x^(1/2)) dx

You can also dirrectly evaluate the limit when the serie tend to infinite but I haven't found any way to match with the answers... (1. Divergent 2. Convergent 3. Divergent)

The #1 when x tend to infinite, 1/x tend to zero thus sin(1/x) tend to zero also... The serie should be converging if so ?!?!

The #2 should give me an integral like this one:

1/(-2)^2 (-2x-1)e^(-2x) + C

-1/4 * (2x+1)e^(-2x) + C

But you can see right away if you evaluate the integral that it tends to infinite which is not converging

For the two others I have no idea! Any help is welcome thanks!

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# Homework Help: Need help for three integrals

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