Question

FAST LIMIT !

Answer 1

ok

Answer 2

\[\lim_{x \rightarrow \infty}(\frac{ x+15 }{ x+3 })^{\ln(\sin \frac{ 1 }{ x })}\]

Answer 3

@ganeshie8 @Abhisar @Callisto @Compassionate @uri @Kainui @eliassaab @inkyvoyd
@Joel_the_boss @Coolsector @Amistre64 @TheSmartOne @bibby @geerky42 @confluxepic @inkyvoyd
@Nnesha @camerondoherty @ParthKohli @Zale101 @poopsiedoodle

Answer 4

@Nnesha sorry It was a mistake

Answer 5

tried that e^ln thing and doing l'hopital ?

Answer 6

@ganeshie8 that method works all the time but it's very annoying I need something simpler

Answer 7

yeah i feel the same

Answer 8

the ln(sin(4/x) is power ?

Answer 9

ln(sin(1/x)) is the power

Answer 10

if you substitute the x in the sin you get when x-> infinte zero

Answer 11

ln (zero) = - infinite;
(x+15/x+3) when x-> inifinite is 1;

Answer 12

1^-infinite = 1;

Answer 13

the answer is 1;

Answer 14

@borak 1^infinite is undetermination case believe me

Answer 15

O.K
I will use the sandwich ;
1< the give data <lim x-> ininfte (x+15)/(x+3) ^ ln(1)
you see sides is 1; then the give is 1 this good way

Answer 16

((x+15)/(x+3)) ^(ln(sin(4/x)) this bigger than 1;
and if we found something bigger than ((x+15)/(x+3)) ^(ln(sin(4/x)) in limit equal to 1 then according to sandwich the give question will e in limit equal 1

Answer 17

\[\lim_{x \rightarrow \infty} (((x+15)/(x+3))^{\ln(1)} = 1\]

Answer 18

this is right side ; and left side is 1

Answer 19

then \[\lim_{x \rightarrow \infty} (((x+15)/(x+3))^{\ln(sin(4/x))} = 1\]
between them !!! then he is equal in limit to 1

Answer 20

Can you prove me it's bigger than 1 ?

Answer 21

which one ?

Answer 22

@borak you found only the right side of the sandwich which is good but I need the left side which can't be 1 (it is a function which tends to be 1 but never it is like in the right side)

Answer 23

the number without the power is bigger that 1 you accept me in this point ?

Answer 24

actually tends to 1

Answer 25

from the right side it's tend yea ?

Answer 26

if it tends to 1 from the right then it's bigger than 1 , and equal to it in the limits

Answer 27

I don't understand what you saying