求极限公式,lim x趋于无穷,sinx/x x/sin1/x lim x趋于0,xsin1/x 1/xsinx xsin1/x

lim x趋于无穷，sinx/x =0 x/sin1/x=sin(1/x)/(1/x)=1
lim x趋于0，xsin1/x = sin(1/x)/(1/x)=0 1/xsinx =无穷

我求的是1，不知道对不对 答案是1。 lim(x→0) [xsin(1/x)+(1/x)sinx] =lim(x→0) xsin(1/x)+lim(x→0) sinx/x，前面一项是(0

lim x趋于无穷 sinx/x=0
lim x趋于无穷 x/sin1/x->无穷/0型还是无穷
lim x趋于无穷 xsin1/x=(sin1/x)/(1/x)=1
lim x趋于0 xsin1/x=0
lim x趋于0 1/xsinx=1

lim_{x->无穷} (1/x) = 0.
lim_{x->无穷} sin(1/x) = 0.
lim_{x->无穷} 1/sin(1/x) = 无穷.
lim_{x->无穷} x/sin(1/x) = 无穷.
|sin(x)|lim_{x->无穷} (1/x)sin(x) = 0. [有界量乘无穷小量还是无穷小量]
lim_{x->0} x = 0.
|sin(1/x)|lim_{x->0} xsin(1/x) = 0. [有界量乘无穷小量还是无穷小量]
lim_{x->0} sin(x) = 0.
lim_{x->0} sin(x)/x = 1.