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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

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