Question

x极限于a+,分子根号x减根号a加根号（x－a）,分母根号(x方-a方) ,求极限

Answer 1

lim[x→a+][√x-√a+√(x-a)]/√(x^2-a^2)

=lim[x→a+](√x-√a)/√(x^2-a^2)+lim[x→a+]1/√(x+a)

=1/√(2a)+lim[x→a+]1/2x^(-1/2)/[x(x^2-a^2)^(-1/2)]

=1/√(2a)+lim[x→a+]1/2(x^2-a^2)^(1/2)/[xx^(1/2)]

=1/√(2a)