Asked by victor.m
Evaluate limit squareroot of (x^4 - 16)/(x^3 - 8) as x approaches 2
Answers
Answered by
drwls
x^4 -16 = (x^2 +4)(x+2)(x-2)
x^3 -8 = (x-2)(x^2 +2x + 4)
The x-2 terms cancel
(x^4-16)/(x^3-8)
= (x^2+4)(x+2)/(x^2+2x+4)
-> 8*4/12 = 8/3 as x -> 2
If you are familiar with calculus, you could also take the ratio of derivatives of numerator and denominator, and get the same answer.
x^3 -8 = (x-2)(x^2 +2x + 4)
The x-2 terms cancel
(x^4-16)/(x^3-8)
= (x^2+4)(x+2)/(x^2+2x+4)
-> 8*4/12 = 8/3 as x -> 2
If you are familiar with calculus, you could also take the ratio of derivatives of numerator and denominator, and get the same answer.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.