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December 22, 2014

December 22, 2014

Posted by **Arthur** on Thursday, January 27, 2011 at 4:39pm.

(a)

3x3 + 9x2 + 9x + 3

x4 + x3 + x + 1

(b)

lim

x → −1

3x3 + 9x2 + 9x + 1

x4 + x3 + x + 1

- Math -
**Reiny**, Thursday, January 27, 2011 at 5:58pmdid you mean

3x^3 + 9x^2 + 9x + 3 ? If so, then

= 3(x+1)(x+1)(x+1)

x^4 + x^3 + x + 1

= x^3(x+1) + (x+1)

= (x+1)(x^3 + 1)

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

so in your limit you would have

lim 3(x+1)^3 / ((x+1)^2(x^2 - x + 1) as x=-1

= lim 3(x+1)/(x^2 - x + 1)

= 0/3 = 0

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