高数极限解答.11.12.二（1）三个题

11.lim[x^2sin(1/x)]/tanx = limxsin(1/x)=0
12.lim[√(1+six)-1]/x^2 = lim(six/2)/x^2 = ∞
1.lim(1-1/2^2)(1-1/3^2)...(1-1/n^2)
= lim(1-1/2)(1-1/3)...(1-1/n)(1+1/2)(1+1/3)...(1+1/n)
= lim(1/2)(2/3)...[(n-1)/n](3/2)(4/3)...{(n+1)/n)]
= lim(1/n)[(n+1)/2] = 1/2.