Asked by Anonymous
Can anyone help me calculate this?
28. lim
x→∞
(e^x + 1)^(1/)x
28. lim
x→∞
(e^x + 1)^(1/)x
Answers
Answered by
Kabe
2.73
Answered by
Reiny
use an intuitive approach
as x --- >∞ , e^x --->∞
so adding 1 to it results in no significant change,
then taking the xth root, will bring you back to e
in effect you are doing (e^x)^(1/x)
= e^(x(1/x)) = e
Kabe approxiated that as 2.73
should have been 2.72 correct to 2 decimals
(2.718281828...)
as x --- >∞ , e^x --->∞
so adding 1 to it results in no significant change,
then taking the xth root, will bring you back to e
in effect you are doing (e^x)^(1/x)
= e^(x(1/x)) = e
Kabe approxiated that as 2.73
should have been 2.72 correct to 2 decimals
(2.718281828...)
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