Please help! Find the limit as x approaches infinity of (1+(6/x))^x
Stacey Warren - Expert brainly.com
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easy to see; as x becomes larger and larger, notice what happens to 6/x. (ignore the exponent for the moment)
6/1 = 6.
6/2 = 3
6/6 = 1
6/12 = 1/2
6/100 = 3/50
6/600 = 1/100
6/1000 = 1/1000
basically, as 6/x where x -> infinity, the value of 6/x will approach zero.
so basically that means we have
well thats easy to simplify
and 1 to any exponent is just 1..
1^2 = 1
1^10000000000000 = 1
etc. so thus the answer is 1.
Your reasoning makes sense! But when I submit it, it says its wrong.. I don't know if there is another way of solving it..?
The section we are working on is dealing with series. I know the fxn converges, so there has to be a set number that it goes to, but it isn't one...
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it's definitely not 1, wolfram says its e^6, i see why but don't quite understand the reasoning they give.
if you want to see.
(1+1/x)^x = e, and 6/x = e^6 i believe, not immediately sure why though
Oh..they raised it to the e and then did ln(fxn)..im assuming.? Haha but thank you so much for your help!!! It was greatly appreciated!!! (((: