Hard Calc Problem

Discus: SAT/ACT Tests and Test Preparation: October 2003 Archive: Hard Calc Problem
 By Mastamac (Mastamac) on Tuesday, October 14, 2003 - 11:00 am: Edit

Find the limit as x approaches infinity of (x-(sqrt(x^2)+x))

Please show how you did it

 By Volleygenius (Volleygenius) on Tuesday, October 14, 2003 - 12:33 pm: Edit

if i am reading this right, then it should simplify to the sqrt(x^2) which is just the absolute value of x. so as x approaches infinity, so does y. hopefully i am reading the equation right.

 By Mastamac (Mastamac) on Tuesday, October 14, 2003 - 08:23 pm: Edit

no the whole term (x^2)+x is under the sqrt

 By Vpasri (Vpasri) on Tuesday, October 14, 2003 - 08:53 pm: Edit

mulitipy (x-sqrt(x^2 +x)) by [x + sqrt(x^2 + x)]/
[x + sqrt(x^2 + x)]

You get: limit as x approaches infinite of
[-x]/[x + sqrt(x^2 + x)]

Since you are taking the limit as this function approaches infinite, the x term under the radical drops out (since it is not the leading term - the highest powered term is quoted the most "influential" term) and you are left with:
limit as x approaches infinite of
[-x]/[x + sqrt(x^2)]=
limit as x approaches of infinite of
[-x]/[2x]
Since the degrees of the numerator and denominator are equal (or since the x's cancel out), the limit simplifies to -1/2

 By Mastamac (Mastamac) on Tuesday, October 14, 2003 - 09:47 pm: Edit

thank you i got as far as the part until the less influential x term drops out