lim x-> 1 (x-1)/(lnx-sinpi x) thank you and include the pi sign in your explanat

Question

lim x-> 1 (x-1)/(lnx-sinpi x) thank you and include the pi sign in your explanation. i couldn't find said sign on the mac computer.

Explanation / Answer

x > 1 ln(x)/sin(pi*x) >>>>>>>> (0/0 form) L Hospital x > 1 [1/x] / [pi cos (pi*x)] x > 1 [1 / (pi x * cos (pi*x))] apply limit [1 / (pi *1 * cos (pi*1))] = 1 / (pi)* (-1) = -1/pi ==================== x > 8 ln[ln(x)] / x >>>>>>>> (inf/inf form) x = e^y as x tends to infinity, y tends to infinity y > inf ln[y)] /(e^y) Hospital > y > inf (1/y) /(e^y) y > inf e^-y/y Hospital > y > inf - e^-y/1 y > inf - [1/e^y] apply limit = - [1/infinity] = 0

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