Thread: limits

please see the attatchment

As x gets indefinetly large 1/x will get closer and closer to zero and any non zero real number rasied to the zero power yeilds one so the lim as x-->infinity of (x)^(1/x) = 1

Originally Posted by bobby77

please see the attatchment

You are asking - what is:



with a choice of answers

Consider:

,

which is equal to:

.

Now if you know that grows more slowly than any
positive power of you are done, as:

,

and so:

.

If you don't know that grows more slowly than any
positive power of , then you can get the same result by a slightly
convoluted application of L'Hopital rule.

RonL

Originally Posted by mathproblem

As x gets indefinetly large 1/x will get closer and closer to zero and any non zero real number rasied to the zero power yeilds one so the lim as x-->infinity of (x)^(1/x) = 1

Would not the same argument apply to ?

RonL