Question

EVALUATE ..... =_=

Answer 1

\[ \lim_{x \rightarrow \infty} ( 1+ \frac{ 3 }{x })^{x}\]

Answer 2

in the future put the question in the question box please

Answer 3

oh yay. this is one of those derpy ones. go look at the definition of e ;)

Answer 4

>_ >

Answer 5

do you know the standard limit formula,
\(\lim_{x \rightarrow 0} ( 1+ x)^{1/x}=...?\)

Answer 6

no
thats new

Answer 7

to bring it in that form, first you need to put x=1/y
so that as x->infinity, y->0

Answer 8

\[\lim_{x \rightarrow 0} ( 1+ x)^{1/x}=e\]

Answer 9

is that a rule !!! we just follow it

Answer 10

put x=1/y
what u get ?

Answer 11

yes, but your Q is not exactly that rule/formula..so answer isn't =e

Answer 12

I got ∞ as an answer

Answer 13

i got one as answer -.-

Answer 14

how 1 ?

Answer 15

both are incorrect :P

Answer 16

i will show u :] .. simple and smart

Answer 17

*waiting eagerly*

Answer 18

:3

Answer 19

\[limx→∞(1+3x)^x \]

\[=(1+\frac{ 3 }{ \infty } )^{\infty} \]

\[= 1^{\infty} = 1\]

Answer 20

:)

Answer 21

lol

Answer 22

exactly

Answer 23

1^infinity is undefined...

Answer 24

:I who said that

Answer 25

try it on ur calculator >:[

Answer 26

i did now......and all the mathematicians did it already..

Answer 27

trust me 1^infinity is not defined...

Answer 28

tell me what u get after u put x=1/y

Answer 29

okie -.-

Answer 30

so the answer is ?

Answer 31

you want answer or you want to know how to get it ?

Answer 32

de second choice

Answer 33

tell me what u get after u put x=1/y

Answer 34

what is y ?

Answer 35

function ?

Answer 36

a new vaiable so that i can bring your limit in standard form.

Answer 37

*variable

Answer 38

in your limit, x-> infinity
standard form, x->0
so i put x=1/y
so that y->0 now..

Answer 39

y = ( 1+ 3/x) ?

Answer 40

=.=

Answer 41

you can choose any variable to put in place of 1/x
'y' or 'u' or 't' or even 'Alice_Dump'
Alice_Dump = 1/x
Alice_Dump ->0

Answer 42

xDD

Answer 43

bdw, y=1/x

Answer 44

okie

Answer 45

so, your limit in terms of y is ?

Answer 46

TT^TT

Answer 47

just let me me think okie -.-

Answer 48

sure, take your time :)

Answer 49

is it ......


\[\frac{ 1 }{ 1+ \frac{ 3 }{x } }\] ??

Answer 50

is that what u mean .!!

Answer 51

-.....-

Answer 52

no...

Answer 53

XD

Answer 54

-.-

Answer 55

im still looking for it too...

Answer 56

i give up thinking -_-

Answer 57

show me de solution

Answer 58

3/x = 3(1/x) = 3y
so, wait....

Answer 59

and i'll seee how u did it

Answer 60

ohh okie ..

Answer 61

i get it now

Answer 62

\[\lim_{x \rightarrow \infty} ( 1+ \frac{ 3 }{x })^{x}\\=\lim_{y \rightarrow 0} ( 1+ 3y )^{1/y} \\ =\lim_{y \rightarrow 0} [( 1+ 3y )^{1/3y}]^3\]
did you get the last step ??

Answer 63

i got the answer e^3

Answer 64

So its multiplied?

Answer 65

e^3 is correct!

Answer 66

food :)

Answer 67

i meant good :) lol

Answer 68

YAY alice got it

Answer 69

O3O thanks to u

Answer 70

xD

Answer 71

X3 i fail

Answer 72

congrats guys! :D