lim n趋近无穷大n^2*(2-n*sin 2/n)=?

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limn趋近无穷大n^2*(2-n*sin2/n)=?limn趋近无穷大n^2*(2-n*sin2/n)=?limn趋近无穷大n^2*(2-n*sin2/n)=?令t=1/n,t->0+原式=lim(

lim n趋近无穷大n^2*(2-n*sin 2/n)=?
lim n趋近无穷大n^2*(2-n*sin 2/n)=?

lim n趋近无穷大n^2*(2-n*sin 2/n)=?
令 t = 1/n,t->0+
原式= lim(t->0) [ 2 - sin(2t) / t ] / t²
= lim(t->0) [ 2t - sin(2t) ] / t³
= lim(t->0) [ 2 - 2 cos(2t) ] / (3t²) 洛必达法则
= lim(t->0) 4sin(2t) / (6t)
= 8/6 = 4/3

4/3
syms x ;
v=x^2*(2-x*sin(2/x));
limit(v,x,inf)