Limits need help?? struggling
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Limits need help?? struggling

[From: ] [author: ] [Date: 12-07-14] [Hit: ]
you have a difference of two squares and in the denominator, a difference of two cubes.Again, a difference of squares in the numerator.(x - 3) cancels out.As x goes to 3.......
limit as x approaches 3

x^4-81 / x^3-27

i need to get the answer without using l'hosptial rule thank you to anyone that is willing to help!!!

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lim x → 3 (x^4 - 81)/(x^3 - 27)

Note that in the numerator, you have a difference of two squares and in the denominator, a difference of two cubes.

lim x → 3 [(x² - 9)(x² + 9)]/[(x - 3)(x² + 3x + 9)]

Again, a difference of squares in the numerator.

lim x → 3 [(x + 3)(x - 3)(x² + 9)]/[(x - 3)(x² + 3x + 9)]

(x - 3) cancels out.

lim x → 3 [(x + 3)(x² + 9)]/(x² + 3x + 9)

As x goes to 3...

(6 * 18)/(9 + 9 + 9)
= 4

Therefore, the limit is 4.
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