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Limits

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Submitted By koko101
Words 270
Pages 2
Find the limit
2) Lim┬(x→2)⁡〖(x^3-8)/(x^2-4)〗
First you use synthetic division to find the two factors of the equation. You will divide by the number 2 because that’s the number x approaches. You have to get the coefficients of each term including x^2 and x even though they aren’t part of the equation. Once you write it out it should look like 2 1 0 0 -8. You bring down the first term and multiply it by 2, the result you will then add to 0. After that you multiply the result of 0+2 to the 2 you rare dividing by. The result you add it to the other 0. The result of 0+4 you once again multiply by the 2 you are dividing by and you end up with 8. The last terms cancel because you add a negative and positive 8. By the end you are left with 1 2 4 0. That is one of the factors but you have to start the factor with one degree less than the original equation. It will be (x^2+2x+4). The other factor will be like your limit except the number will be the opposite (x-2). Once you factor out the denominator from the original equation, you get (x+2) and (x-2) because x^2-4 is a difference of squares. Both (x-2) from the numerator and denominator cancel each other out. After you just plug in the 2 for your x’s and at the end you simplify and get an answer of 3.

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