当n趋于无穷大时,求(an+b)^(c/n)的极限a,b,c为常数

Question

当n趋于无穷大时,求(an+b)^(c/n)的极限
a,b,c为常数

Answer 1

lim(ax+b)^(c/x) = lime^[(c/x)ln(ax+b)]
= lime^[cln(ax+b)/x] (∞/∞)
= lime^[ac/(ax+b)]/1 = e^0 = 1.
则 lim(an+b)^(c/n) = 1.