Question

证明：x趋近于2时,x^2的极限等于4

Answer 1

lim(x-->2) (x^2 - 4) = lim(x-->2) (x+2)*(x-2)

因为x+2和x-2在x-->2连续,所以lim(x-->2) (x+2)*(x-2) = lim(x-->2) (x+2)* lim(x-->2) (x-2) = (2+2)*(2-2) = 0

所以lim(x-->2) (x^2 - 4) = 0

即当x趋近于2时,x^2的极限等于4