Asked by Dalia
Find the following limit if it exists, or explain why it does not exist:
lim as x approaches -infinity of square root of (9x^6-x^2) divided by x^3+5
lim as x approaches -infinity of square root of (9x^6-x^2) divided by x^3+5
Answers
Answered by
Steve
lim x->-∞ √(9x^6-x^2)/(x^3+5) = ∞/∞ so we use derivatives a few times to get
As x gets huge, f(x) just looks like
√9x^6 / x^3 = -3
to get formal,
-lim √[(9x^6-x^2)/(x^6+10x^3+25)]
= √ lim [(9x^6-x^2)/(x^6+10x^3+25)]
Now use l'Hospital's Rule 3 times to evaluate the limit inside the radical
As x gets huge, f(x) just looks like
√9x^6 / x^3 = -3
to get formal,
-lim √[(9x^6-x^2)/(x^6+10x^3+25)]
= √ lim [(9x^6-x^2)/(x^6+10x^3+25)]
Now use l'Hospital's Rule 3 times to evaluate the limit inside the radical
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