We are given the integral
We are then asked to explain, intuitively, what happens to the length of the interval (a,b) as a approaches infinity.
Intuitively, the interval is getting shorter and shorter as a goes to infinity. Easy enough, but here's where I'm stuck. We then are asked to mathematically justify this by finding
We are given a hint that is to write either a or b in terms of the other, then write the expression in terms of one variable before taking the limit. Sounds easy, but this is what I've got so far.
Plugging this back in and evaluating the limit is where I get stuck.
I'm not really sure how to evaluate this limit.
Is there something to be done here by stating that
I don't know where to go with this. Is there some fancy completing the cube action that has to take place to get that a^3 out of the radical?
Seems to lead nowhere.
Am I at least on the right track? Or am I completely setting this up wrong?
Who woulda thought I'd be asked to mathematically justify something in a math class. Doh!