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What is the limit of 10x^(6/x) as x goes to infinity using L Hopital s Rule?
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- kbLv 72 years ago
Let L = lim(x→∞) x^(6/x).
Take the natural log of both sides:
ln L = lim(x→∞) ln(x^(6/x))
.......= lim(x→∞) (6/x) ln x
.......= lim(x→∞) 6 ln(x)/x
.......= lim(x→∞) 6 (1/x)/1, by L'Hopital's Rule (∞/∞ type)
.......= 0.
So, L = e^0 = 1.
Finally, lim(x→∞) 10x^(6/x) = 10 * 1 = 10.
I hope this helps!
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