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Numerade Educator

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Problem 7 Medium Difficulty

Evaluate the limit and justify each step by indicating the appropriate Limit Law(s).

$ \displaystyle \lim_{x \to 8}(1 + \sqrt[3]{x})(2 - 6x^2 + x^3) $

Answer

390

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Video Transcript

to develop this limit. We begin by applying the limit of a product. And so we have The limit as x approaches eight of one plus the cube rid of X. This times The limit as x approaches eight of 2 -6 x squared plus x rays to the third power Next you want to apply the limit of a sum and difference. And so we have The limit as x approaches eight of 1 plus The limit as x approaches eight of the key road of X. These times the limit as X approaches eight of two minus the limit as X approaches eight of 6 x squared Plus, we have the limit as x approaches eight of x rays to the third power. And then from here we want to apply the LTD a constant our route and power. And so from here we have one plus the cube root of the limit of X As X approaches eight and in these times We have two You have six times the limit of X as X approaches eight and then squared plus we have the limit as X approaches aid of x rays to the third power And so we have one plus to rid of eight. This times 2 -6 times it's squared plus we have eight raised to the 3rd power and so simplifying. We have one plus two times 2 -384 Plus 512. This will give us a value of 390 and so this is the value of the limits