Advanced Math/limits

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Expert: - 8/8/2006


Question
how do i solve

lim     1-x²
x->1   ________
      x²+5x-6  

Answer
The problem with (1-x^2)/(x^2 + 5x - 6) is if you let x=1 , you get 0/0 , which is undefined and doesn't tell you anything about the limit.

But if you factor

1-x^2 = (1-x)(1+x)

x^2+5x-6 = (x+6)(x-1)

then

(1-x^2)/(x^2 + 5x - 6) =


(1-x)(1+x) /(x+6)(x-1) =

-(1+x)/(x+6)

now you can just plug in x=1 and get

-2/7

The limit is -2/7

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I can answer any questions from the standard four semester Calulus sequence. Derivatives, partial derivatives, chain rule, single and multiple integrals, change of variable, sequences and series, vector integration (Green`s Theorem, Stokes, and Gauss) and applications. Pre-Calculus, Linear Algebra and Finite Math questions are also welcome.

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