Question

anyone please find limit x approach to infinity [(x+2)/(x+1)]^x ?
thanks

Answer 1

read this: http://www.mathsisfun.com/calculus/limits-infinity.html
gives a nice detailed explanation on this stuff.

Answer 2

\(\large \lim \limits_{x \to \infty }\left( \frac{x+2}{x+1}\right)^x\)

\(\large \lim \limits_{x \to \infty }e^ {\ln \left( \frac{x+2}{x+1}\right)^x}\)

\(\large e^ {\lim \limits_{x \to \infty } \ln \left( \frac{x+2}{x+1}\right)^x}\)

\(\large e^ {\lim \limits_{x \to \infty } x\ln \left( \frac{x+2}{x+1}\right)}\)

Answer 3

okay..thank you very much... :-*

Answer 4

np :) thats not all.... still so much to do ;)

Answer 5

yaa okay.. i'll try find the answer.. ;)

Answer 6

one easy way is to use the known limit : lim x-> inf (x+1/x)^x = e

Answer 7

substitute x+1 =t, and convert the given limit to that form and conclude

Answer 8

((x+1+1)/(x+1))^x
= (1 + 1/(x+1))^x+1-1
= (1 + 1/(x+1))^x+1 * (1 + 1/(x+1))^-1

lim x->~ (1 + 1/(x+1))^x+1 * (1 + 1/(x+1))^-1
= limx->~ (1 + 1/(x+1))^x+1 * limx->~ (1 + 1/(x+1))^-1
now you can identify that what's the answer then ...

Answer 9

okay..thank you yaa... ;) ;)

Answer 10

sepertinya anda orang melayu, ya :v
are you from malaysian or indonesian ??

Answer 11

hahaha iyaaaa..malaysia..makasih yaa..

Answer 12

okay, kita bertetangga :)
saye dri indonesia

Answer 13

oh..indonesia.. met kenalan yaa.. makasih sekali lagi buat jawapannya..

Answer 14

jadi, apa jawabanmu adik manis, adik comel ?

Answer 15

ini soalan dari adik saya..dia sedang jawab.. ;)