Question

关于三个求极限的问题，都忘光了，求高手解答，谢谢！

Answer 1

16.
即t=x-1
t->0
lim (tan t-sin t)/t
=lim (sint-sintcost)/(tcost)
=lim sint(1-cost)/(tcost)
=lim sint/t *lim (1-cost)/cost
=1*0
=0

17.
1/k(k+1)(k+2)
=[(k+2)-(k+1)]/k(k+1)(k+2)
=1/k(k+1)-1/k(k+2)
=1/k-1/(k+1)-(1/2)[1/k-1/(k+2)]
累加
=1/1-1/2-(1/2)[1/1-1/3]
+1/2-1/3-(1/2)[1/2-1/4]
+...
+1/k-1/(k+1)-(1/2)[1/k-1/(k+2)]
第一个累加中间项都消去
=1/1-1/(k+1)-(1/2)[1/1+1/2-1/(k+1)-1/(k+2)]
取极限
=1-(1/2)(1+1/2)
=1/4

18.
|4-1/10*N-4|<1/101

1/10N<1/101
10N>101
N>10.1
N>=11