Question

please help

Answer 1

\[\lim_{x \rightarrow 1} x ^{1/(x-1)}\]

Answer 2

use logarithms to find the limit

Answer 3

let L=lim ....
taking log
ln L = lim ...
=lim 1/(x-1) . ln x
can u use L'Hoptals here ?

Answer 4

it said use logarithms

Answer 5

'taking log'
means u sing log

Answer 6

so it would be ln x/(x-1)
then i will apply the LHs rule?

Answer 7

yes, if u can

Answer 8

is there another way of getting the limits??

Answer 9

yes, put x-1 = y

Answer 10

then??

Answer 11

use limit y->0 ln(1+y)/y = 1
standard formula.

Answer 12

ok thx
i will try them both

Answer 13

welcome :)

Answer 14

another question sir

show that the grap of the function f(x) = lnx/x has a maximum at x=e , a point of inflection at x = e^3/2, approaches minus infinity as x approaches zero through positive values, and approaches zero as x approaches plus infinty.

Answer 15

which part are u stuck at ?

Answer 16

proving that the maximum is at e

Answer 17

the derivatives that i get was 1-lnx/x^2

Answer 18

if u equate that to 0
u get lnx =1
so x=e.........

Answer 19

to get the max val. 0<1 < 2
substitute to the equation
then determine if its + to -