Question

i ned someone to teach me improper integrals

Answer 1

do you have a particular problem you're stuck with?

Answer 2

yes, bounds from 1 to infinity. f(x)=(2+e^-x)/x. use comparison test to determine if its divergent or convergent

Answer 3

In the given domain/bounds x is positive, which is a good thing, you can therefore say that\[\Large x>0  \text{and} \ e^{-x}>0 \]
Furthermore, \(e^{-x}\) doesn't get too large, so you can remove it and say:
\[\Large \frac{2}{x}<\frac{2+e^{-x}}{x} \]
we could argue about how important the 2 is, it doesn't really add much to the problem or our argument, as far as it comes to me, it doesn't hurt keeping it at this point.

Answer 4

By the integral test you can tell that 2/x diverges, what does that tell you about your original statement?

Answer 5

okay i understand now. so does it mean i should always ignore the function which doesn't get large?

Answer 6

how about tan^-1(x)/(2+e^x) divergent or convergent?

Answer 7

it's not as simple as that unfortunately to just ignore a term, but it's in the word itself, the comparison test means that you compare with another sum of which you can tell whether it's convergent or divergent.

Answer 8

but you can try the same logic on this on, for instance \(\tan^{-1}(x)\) doesn't get too big, it's maximum value is 90° or pi/2