Question

use the limit comparison theorem to determine if the following integral diverges or converges:

integral from 2 to infinite: (x^2 dx)/[(x-1)^2 * (x+3)]

Answer 1

This is how I'm reading the integral given, the integral of {(x^2)/[(x-1)(x-1)(x+3)]} dx from 2 to a as a grows unbounded (or approaches infinity as many like to say).

When x=2, (x^2)/[(x-1)(x-1)(x+3)] is 4/5, and this value is the initial point of the integral. This means this 4/5 is less than or equal to the integral over our given bounds (2+) since the derivative of the polynomial is positive over the same bounds of integration so the integral is constantly getting a little positive addition to it.

The integral of 4/5 over the same bound clearly grows unbounded or diverges, and since the integral of 4/5 is smaller at every point within the bounds of integration than the given integral, then the given integral must diverge too.

Answer 2

mary beth and steve like to shop at a warehouse store .they get a 10% discount on everything they buy.what fractional part of the disscount do they recieve?
a.1/20
b.1/10
c.1/510
d.1/520