CAS problem with solution

[Mark Hardman]

(03-04-2015 09:14 PM)Teresa Wrote:  Hello all, I just bought a Prime and tried some things out. So I tried to get a solution in CAS mode for the equation lim X->infinity of (sqrt(X*X+2X+1)-sqrt(X*X)). I think the solution should be 1 but i get -infinity.
The plot of the function gives also 1. I tried it in the simulator (rev6975) and the calculator (rev.6975 CASvers. 1.1.2-11) same result.
What do i do wrong?
Thanks for your help Teresa

WolframAlpha would agree with your answer:

limit(v(x^2+2*x+1)-vx^2,x,8)

If you give the CAS just a little bit of help, it will give you the correct answer:



It seems a bit odd that the CAS doesn't perform the trivial reduction of √x^2 = x. Perhaps it's reducing it to |x|. But even that shouldn't change the solution. Though, depending on the direction of the limit, the answer might be -1 or 1: