Question

微积分求极限

lim（x趋向无穷）(x2+(cosx)2-1)/(x+sinx)2=
请写明步骤

Answer 1

lim（x->oo）(x^2+(cosx)^2-1)/(x+sinx)^2
=lim（x->oo）(x^2-(sinx)^2)/(x+sinx)^2
分子分母同除以xsinx得到：
=lim（x->oo）(x/sinx-sinx/x)/(x/sinx+sinx/x+2)
=lim（x->oo）(x/sinx+sinx/x+2-2-2sinx/x)/(x/sinx+sinx/x+2)
=1-2[1/(oo+0+2)]
=1