(9)
lim(x->4) [√(2x+1)-3]/(√(x-2) -√2]
=lim(x->4) [√(2x+1)-3].(√(x-2) +√2] /(x-4) ( 有理化分母)
=(2√2) lim(x->4) [√(2x+1)-3]/(x-4)
=(2√2)lim(x->4) (2x-8)/ { (x-4).[√(2x+1)+3] } ( 有理化分子)
=(√2/3)lim(x->4) (2x-8)/ (x-4)
=2√2/3
(10)
lim(n->∞) (1+ 1/2+1/2^2+...+1/2^n)
=lim(n->∞) 2(1- 1/2^(n+1))
=2