lim〔a-√（a^2+x^2）〕/x^2 x→0

网友回答

lim(x→0) [a-√(a^2+x^2)]/x^2
=lim(x→0) [a-√(a^2+x^2)] *[a+√(a^2+x^2)] / x^2[a+√(a^2+x^2)]
=lim(x→0) (a^2-a^2-x^2) / x^2[a+√(a^2+x^2)]
=lim(x→0) -x^2 / x^2[a+√(a^2+x^2)]
=lim(x→0) -1/ [a+√(a^2+x^2)] 代入x=0
= -1/2a
所以极限值为 -1/2a