(1)x³为高阶无穷小，∴极限=0
(2)lim(x→∞)[sin(1/x)+cos(1/x)]^x
令t=1/x,t→0
原极限=lim(t→0)(sint+cost)^(1/t)
=lim(t→0)[1+(sint+cost-1)]^{[1/(sint+cost-1)]·(sint+cost-1)/t}
∵lim(t→0)(sint+cost-1)/t=lim(t→0)(cost-sint)=1 洛必达法则
∴原极限=lim(t→0)[1+(sint+cost-1)]^[1/(sint+cost-1)]=e
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