求下列极限：1.lim(x→2)(x+2/x-2) 2.lim(x→0)4x^3-2x^2+x^2-2x)
问题描述：
求下列极限：1.lim(x→2)(x+2/x-2) 2.lim(x→0)4x^3-2x^2+x^2-2x)
3.lim(x→0)tanx-sinx/x^3
4.lim(x→π)sin3x/x-π
5.lim(x→无穷大量）（1-1/2x)^x+2
知道答案,求过程!谢谢
答
3.lim(x→0)[(tanx-sinx)/x^3]=lim(x→0)[sinx(1-cosx)/(x³cosx)]=lim(x→0){(sinx/x)*[sin(x/2)/(x/2)]²*[1/(2cosx)]}=[lim(x→0)(sinx/x)]*{lim(x→0)[sin(x/2)/(x/2)]}²*{lim(x→0)[1/(2cosx)]}=1...3. =3*lim(x→π)[sin(3(x-π))/(3(x-π))] (应用诱导公式) 这一部我不懂lim(x→π)[sin(3(π+x-π))/(x-π)]=lim(x→π)[3*sin(3(π+x-π))/(3(x-π))] (分子分母同乘3，且x=π+x-π)=3*lim(x→π)[sin(3π+3(x-π))/(3(x-π))] =3*lim(x→π)[sin(3(x-π))/(3(x-π))] (应用诱导公式,即sin(3π+3(x-π))=sin(3(x-π)))