Solving Improper Integrals: $\int_2^{inf} \frac{2}{(x+3)^{3/2}}$

[ProBasket]

$$\int_2^{inf} \frac{2}{(x+3)^{3/2}}$$

integrating the problem, i get:
$$\frac{-4}{sqrt(x+3)}$$

now integrating from 2 to inf(replaced with b), plugging in 2, i get -4/5:
f(b) + 4/5
lim->inf

it looks like f(b), lim->inf goes to -4 X 10^-inf

so wouldn't the answer just be divergent? i also tried 4/5 and -4/5, but it wouldn't work. i don't really know the proper way to find the limit. all i do is plug in the largests number and try to find a pattern.

 

[Curious3141]

What is $$lim_{x \rightarrow \infty}\frac{1}{x^n}$$ where n is any positive real number ?

 

[ProBasket]

looks like it goes to zero

 

[dextercioby]

Yes,that's right...

Daniel.

 

[ProBasket]

yes, but i still don't get it... what are you trying to tell me?


are you saying that f(b),lim->inf goes to zero? and the answer should be 4/5?

 

[dextercioby]

Exactly.

Daniel.

 

[ProBasket]

ah, thanks for the help. actually, f(2) is not equal to 4/5, i typed it wrong in my calculator. i need some sleep, thanks agian.

 

[dextercioby]

I realize that i didn't bother to do the calcuation for you and that's why i agreed with you...

Daniel.