lim(x+a^x)^1/x=?x趋向于0 (a>0)
问题描述:
lim(x+a^x)^1/x=?x趋向于0 (a>0)
答
∵lim(x->0)[ln(x+a^x)/x]=lim(x->0)[(1+lna*a^x)/(x+a^x)](0/0型极限,应用罗比达法则)=(1+lna*1)/(0+1)=1+lna ∴原...
lim(x+a^x)^1/x=?x趋向于0 (a>0)
∵lim(x->0)[ln(x+a^x)/x]=lim(x->0)[(1+lna*a^x)/(x+a^x)](0/0型极限,应用罗比达法则)=(1+lna*1)/(0+1)=1+lna ∴原...