Question

some one can solve this...lim ((arctanx/x)/lnx)
x→∞
some one can solve this...lim ((arctanx/x)/lnx)
x→∞
@Mathematics

Answer 1

\[\lim_{x\to\infty}\frac{\frac{\arctan x}{x}}{\ln x}.\]This?

Answer 2

yes

Answer 3

Well, this can be rewritten as\[\lim_{x\to\infty}\frac{\arctan x}{x\ln x}\implies\lim_{x\to\infty}\frac{\arctan x}{\ln x^x}.\]The limit of the arctangent as this approaches infinity is pi/2, and the limit of ln x^x as this approaches infinity is infinity. Therefore, the limit of the whole function is 0.

Answer 4

is that your answer

Answer 5

i think the answer is pi/2

Answer 6

\[\lim_{x\to\infty}\arctan x=\frac{\pi}{2}.\]\[\lim_{x\to\infty}x\ln x=\infty.\]

Answer 7

you have to use L`hopital regel,,,,and you will get pi/2

Answer 8

Ich habe denn keine Ahnung, was deine ursprüngliche Frage ist.

Answer 9

Oh....i cant speak duch

Answer 10

Und warum benutzt du die Regel von L'Hospital, wenn der Limes des Zählers existiert?

Answer 11

Why are you using L'Hôpital's rule when the limit of the numerator exists?

Answer 12

let me ask you whre u from,,?

Answer 13

I'm German.

Answer 14

iam from norway,,

Answer 15

wenn Sie sehen, der Zähler des Ausdrucks, so dass Sie unendliche x 0 haben

Answer 16

Ich konnte das nicht verstehen. Aber man kann nur diese Regel benutzen, wenn man das hat:
\[\lim_{x\to c}f(x)=\lim_{x\to c}g(x)=0,\]oder\[\lim_{x\to c}f(x)=\lim_{x\to c}g(x)=\pm\infty,\]und\[\lim_{x\to c}\frac{f'(x)}{g'(x)}\]existiert.

Answer 17

look the quation again,,,and how it writens,,,

Answer 18

i mean before you take x to the numinator

Answer 19

prove that limx→∞ (arctanx/x ) = ∞. solve this one