Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
Please help calculating this limit?
Limit (when x tends towards 8) of:
(x - 8) / (x^(1/3) - 2)
2 Answers
- Gia huy HoLv 56 years agoFavorite Answer
Let x=u^3
If x approaches to 8, then u approaches to 2
->(u^3-8)/(u-2)
->(u-2)(u^2+2u+4)/(u-2)
->(u^2+2u+4)
As u approaches 2, 2^2+2*2+4=12
- husoskiLv 76 years ago
Factor the numerator as a difference of cubes:
x - 8 = [x^(1/3)]^3 - 2^3 = [x^(1/3) - 2] [x^(2/3) + 2x^(1/3) + 4]
(x - 8) / [x^(1/3) - 2] = x^(2/3) + 2x^(1/3) + 4
The discontinuity was removable and the limit as x-->8 is 4 + 2(2) + 4 = 12
