Thread: Question about Limits involving infinity

The problem is: evaluate the limit as x approaches infinity of [x-sqrt(x)]. What I did was multiply that by [x+sqrt(x)]/[x+sqrt(x)] to get (x^2-x)/[x+sqrt(x)], i then factored an x out of the top, getting [x(x-1)]/sqrt(x). Then, since the degree of the numerator is higher, I said that the limit is infinity. I know that I got the right answer, but did I do the problem in the correct way?

Is...

(1)

... and the You have to valuate the limit for of (1)...

Kind regards

Originally Posted by jem163

The problem is: evaluate the limit as x approaches infinity of [x-sqrt(x)]. What I did was multiply that by [x+sqrt(x)]/[x+sqrt(x)] to get (x^2-x)/[x+sqrt(x)], i then factored an x out of the top, getting [x(x-1)]/sqrt(x). Then, since the degree of the numerator is higher, I said that the limit is infinity. I know that I got the right answer, but did I do the problem in the correct way?

Your calculations are valid, although most of the work is unnecessary to be honest. You can consider the original expression as



Clearly already the numerator is higher degree than the denominator, and the term is the term of highest degree in the numerator, so it defines the end-behavior.