CAS problem with solution

[Mark Hardman]

(03-04-2015 10:20 PM)Tim Wessman Wrote:  Interestingly enough, the equation as you have it written does actually work. The ^2 seems to be doing something strange here.

limit(√(x*x+2*x+1)-(√(x*x)),x,∞) ----> 1
limit(√(x^2+2*x+1)-(√(x^2)),x,∞) ----> -∞

The CAS must be reducing the √(x^2) to just x (rather than |x|). In that case, the limit as x--> -∞ would be -∞:



But, regardless of which direction you force the limit it always gives the limit as x goes to -∞:

limit(√(x^2+2*x+1)-(√(x^2)),x,∞,-1) = -∞
limit(√(x^2+2*x+1)-(√(x^2)),x,∞,1) = -∞