Question

lim((arctanx+π)/(x+2)) x趋向无穷

Answer 1

x→-∞,arctanx→-π/2

lim(x→-∞)((arctanx+π)/(x+2)) =lim(x→-∞)(π/2)/[x+2]=0

x→-∞,arctanx→π/2

lim(x→+∞)((arctanx+π)/(x+2)) =lim(x→+∞)(3π/2)/[x+2]=0

∵lim(x→-∞)f(x)=lim(x→+∞)f(x)=0

∴linm(x→∞）f(x)=0