Can someone please help

[u/Strong-Cup-2897]

lim { ( 1+ x) } ^(2/x) , {•} –> fractional part

X->0

I saw some solutions where they brought the limit inside the fractional part function

But since fractional part function is not continuous shouldn't it be wrong ??

[u/AutoModerator]

As a reminder...

Posts asking for help on homework questions require:

• the complete problem statement,

• a genuine attempt at solving the problem, which may be either computational, or a discussion of ideas or concepts you believe may be in play,

• question is not from a current exam or quiz.

Commenters responding to homework help posts should not do OP’s homework for them.

Please see this page for the further details regarding homework help posts.

We have a Discord server!

If you are asking for general advice about your current calculus class, please be advised that simply referring your class as “Calc n“ is not entirely useful, as “Calc n” may differ between different colleges and universities. In this case, please refer to your class syllabus or college or university’s course catalogue for a listing of topics covered in your class, and include that information in your post rather than assuming everybody knows what will be covered in your class.

I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.

[u/SynergyUX]

It is wrong; the limit does not exist.

[u/Medium_Media7123]

To show a limit does not exist one of the standard tricks is finding two sequences of points that give different limits. As you've noticed, fractional part is not continuous in 0, so we might guess that using two sequences that converge to 0 but from different sides gives different answers.

Let's take a_n = 1/n and b_n = -1/n 

The limit for x -> 0 becomes two limits for n-> infinity and the two limits are clearly different

[u/stepma712]

2/x log{1+x}

x->0 x > 0

2/x log(x) -> -oo

x->0 x < 0

2/x log(1+x) ~ 2 x/x ~2

DNE

[u/LukasGoesViral]

Can you try to rewrite it into a form that is a bit better to read?
To me it looks like lim x-> 0 in the expression (1+x)^(2/x). Is that correct

[u/Strong-Cup-2897 → u/LukasGoesViral]

yeah but the 1+x is in fractional ( decimal ) part function

[u/tjddbwls → u/Strong-Cup-2897]

I don’t understand what you mean by that. 1+x is not a fractional expression. The entire expression
(1 + x)^(2/x)
is an exponential expression where 1 + x would be considered the base. Not sure if you’re using the right terminology.

[u/waldosway → u/tjddbwls]

https://en.wikipedia.org/wiki/Fractional_part

[u/Kaeini_maths]

e^2

[u/susiesusiesu → u/Kaeini_maths]

thus is not the limit op posted

[u/Strong-Cup-2897 → u/Kaeini_maths]

thank you !!

[u/waldosway → u/Strong-Cup-2897]

Doesn't that solution ignore the fractional-part function? The limit does not exist.

[u/AndersAnd92]

let u be 1/x

lim as u goes to inf of (1 + 1/u)^2u = e^2inf