Find the limit using LHospitals RuleSolutionlimx1 x11x apply

Find the limit using L\'Hospital\'s Rule.

Solution

lim_x-1+ x^(1/1-x)

apply L hospital

L = lim_x-1+ (1/1-x) x^(x/ 1-x)

apply L hospital

L = lim_x-1+ - x/(1-x) x^(2x-1/1-x)

L = lim_x-1+ - x^((2x-1/1-x) + 1) /1-x

L = lim_x-1+ -x^(x/1-x) /1-x = -L

=> 2L = 0

=> L = 0

hence lim_x-1+ x^(1/1-x) = 0