求极限：lim[sin(1/x)+cos(1/x)]^x (x趋于正无穷）

lim[sin(1/x)+cos(1/x)]^x (x趋于正无穷） 令t=1/x,当x->正无穷,有:t->0 则:lim(x->正无穷)[sin(1/x)+cos(1/x)]^x =lim(sint+cost)^(1/t) =lim[1+(sint+cost-1)]^{[1/(sint+cost-1)]*(sint+cost-1)/t} 因为:lim(t->0...