Limits

zgall1

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Jun 5, 2005
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Can anybody help with this one?

lim x --> 1 (x^n - 1)/(x-1)

Thanks
 
When I plugged in various values for n, I found that as x --> 1, y approaches infinity. But with the method described above, the limit = 0 (I believe). Where am I going wrong?
 
Hello, zgall1!

]When I plugged in various values for n, I found that as x --> 1, y approaches infinity . ?
But with the method described above, the limit = 0 . ?
Where am I going wrong? . . . everywhere!
You must be "plugging" incorrectly . . .

. . . . . . . . . . . . . . . . .x<sup>5</sup> - 1
Let n = 5: /f(x) . = . --------
. . . . . . . . . . . . . . . . .x - 1

. . . . . . . . . . . . . . . . . . . . .1.0001<sup>5</sup> - 1
. . . Then: . f(1.0001) . = . --------------- . = . 5.001
. . . . . . . . . . . . . . . . . . . . . . 0.0001

. . . . . . . . . . . . . . . . . . . . .0.9999<sup>5</sup> - 1
. . . . And: . f(0.9999) . = . --------------- . = . 4.999
. . . . . . . . . . . . . . . . . . . . . . -0.0001

As x --> 1, the limit seems to be approaching 5.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

With the "described method", we can factor and reduce first.

. . . . (x - 1)(x<sup>4</sup> + x<sup>3</sup> + x<sup>2</sup> + x + 1)
lim . ------------------------------------ . = . lim (x<sup>4</sup> + x<sup>3</sup> + x<sup>2</sup> + x + 1) . = . 5
x->1 . . . . . . . . . . x - 1 . . . . . . . . . . . .x->1
 
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