Hi, I'm confused on how to figure out the problem . I have the problem worked out, but I am having difficulty understanding how to get from step one to step 2: to Thanks for the help in advance.
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It was done using the difference of 2 cubes.
It is just factorisation. For example, If Since , by factor theorem, is a factor. So Do either long division or comparison to get the other quadratic factor, you will get . In your limit problem, my is your
You can do synthetic division: So: 3 | 1 0 0 -27 _ |___3 9 27 ___ 1 3 9 0 hmm don't know how to do this in latex, nor can i get it to line up . . . sorry. So you lower the power thing and: hence:
A slightly different way to do this problem would be to "rationalize" the denominator. Since , [tex](x^{1/3}- 3)(x^{2/3}+ 3x^{1/3}+ 9)= x- 27. Multiplying both numerator and denominator by gives . Now you can let x= 27 in that.
Originally Posted by cynlix Hi, I'm confused on how to figure out the problem . put and the limit becomes which you know how to solve.
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