Q 821349400   用纸写好拍照传神马的最有爱了.

lim(1-cosx)/x^2
=lim2[sin(x/2)]^2/x^2
=lim1/2*[sin(x/2)]^2/(x/2)^2
=1/2*lim[sin(x/2)/(x/2)]^2
=1/2
lim(1-5/x)^(x-1)
=lim(1+t)^(-5/t -1)     注：t = -5/x,则当 x →∞时,t → 0
=lim(1+t)^(-1) * lim[(1+t)^(1/t)]^(-5)
=lim(1+0)^(-1) * [lim(1+t)^(1/t)]^(-5)
=1 * e^(-5)
=e^(-5)
lim[√(x^2+1) - √(x^2-1)]
=lim[√(x^2+1)-√(x^2-1)]*[√(x^2+1) + √(x^2-1)]/[√(x^2+1) + √(x^2-1)] 注：分子、分母同乘以
=lim[(x^2+1) - (x^2 -1)]/√(x^2+1) + √(x^2-1)]
=lim2/[√(x^2+1) + √(x^2-1)]
=0