Question

help please...

I will attach the practice test questions...

Answer 1

Please attach your practice test answers and efforts.

If you really have no idea on any of them, you're toast.

Answer 2

well i worked on # 2 and 3 and i said #2 diverges and #3 converges ?? but i have no idea for # 1 can you helP???

Answer 3

/loser66/ cn you help ?:s

Answer 4

ok firstly calculate \[\int_0^\infty \frac{\tan^{-1}x}{1+x^2} dx\]

Answer 5

Hint: \(\Large\int\frac1{1+x^2}dx=\tan^{-1}x\)

Answer 6

i found it diverges but i'm wrong so if you know the answer cn you please explain it to me step by step???

Answer 7

\[\hspace{15pt}\large\int_0^\infty\frac{\tan^{-1}x}{1+x^2}dx\]\[\Large=\int_0^\infty\tan^{-1}x\hspace{5pt}d(\tan^-1x)\]\[\Large=\frac12\left[\left(\tan^{-1}x\right)^2\right]_0^\infty\]\[\Large=\frac12\left[\left(\frac\pi4\right)^2-0^2\right]\]\[\Large=\frac{\pi^2}{32}\]

Answer 8

Since this is finite, the series therefore converges

Answer 9

thank you so much

Answer 10

no problem :)