Question

Compute
lim xtan (1/x) as x approaches infinity Compute
lim xtan (1/x) as x approaches infinity @Mathematics

Answer 1

its an inderterminate product right?

Answer 2

let u=1/x

take limit as\[u\to0^+\]

Answer 3

use \[\lim_{u\to 0}\frac{sin(u)}{u}=1\]

Answer 4

why is it sin (u) over u

Answer 5

it's not

it's sin(u)/u * cos(u)

= 1 * 1

Answer 6

\[\lim_{u \rightarrow 0}\frac{1}{u}\frac{sinu}{cosu}=\lim_{u \rightarrow 0}\frac{1}{cosu}*\lim_{u \rightarrow 0}\frac{sinu}{u}\]

Answer 7

whoops, 1/cos(u)...yeah

Answer 8

both limit equal one so 1*1=1

Answer 9

just something to note

\[\lim_{x\to\infty}x\tan(1/x)\]

is equivalent to

\[\lim_{u\to0^+}\frac{\tan(u)}{u}=\cdots\]

but showing

\[\lim_{u\to0}\frac{\tan(u)}{u}=1\] will technically work.

Answer 10

so it wasnt an indetermiantae form since it equaled 1? or was it an indeterminate product?

Answer 11

it is an indeterminate form