Question

求极限：lim [√(m+1)-√m]√m lim 4/[√(t^2+3t)-√(t^2+1)]

Answer 1

lim [√(m+1)-√m]√m = lim √m/(√(m+1)+√m) =1/2

lim 4/[√(t^2+3t)-√(t^2+1)]= lim4[√(t^2+3t)+√(t^2+1)]/[(t^2+3t)-(t^2+1)]

=lim4[√(t^2+3t)+√(t^2+1)]/(3t-1)

=lim 4(√(1+3/t)+√(1+1/t)]/(3-1/t)

= 8/3

利用得都是 a^2 - b^2 = (a+b)(a-b)