利用重要极限lim（1+u）^1/u=e求下极限lim[(x+3)/(x-2)]^2x+1谢谢了

Question

利用重要极限lim （1+u）^1/u=e求下极限 lim[(x+3)/(x-2)]^2x+1
谢谢了

Answer 1

lim[(x+3)/(x-2)]^2x+1
=lim[1+5/(x-2)]^2x+1
=lim[1+1/[(x-2)/5]]^[(x-2)/5*(2x+1)*5/(x-2)]
=lime^[5(2x+1)/(x-2)]
=e^10