Asked by Vandit
lim x→0 ((1/x)^(sinx))
Answers
Answered by
Steve
f(x) = (1/x)^(sinx) = 1/(x^sinx)
Let us take the limit as x→0+, since rasning negative numbers to real powers is not well defined.
consider limit x→0 g(x)=x^x
lng = x lnx = lnx/(1/x)
limit ln g(x) as x→0 = (1/x)/(-1/x^2) = -x
limit ln(g(x)) = 0
so, limit g(x) = 1
See what you can do with that, since sinx < x
Let us take the limit as x→0+, since rasning negative numbers to real powers is not well defined.
consider limit x→0 g(x)=x^x
lng = x lnx = lnx/(1/x)
limit ln g(x) as x→0 = (1/x)/(-1/x^2) = -x
limit ln(g(x)) = 0
so, limit g(x) = 1
See what you can do with that, since sinx < x
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.