Question

计算极限数学题LIM X->2 ,分子是 X平方-4,分母是SIN(X-2) 能不能详细说

Answer 1

lim(x->2) (x²-4)/sin(x-2)

=lim(x->2) [(x+2)(x-2)]/sin(x-2)

=lim(x->2) (x+2) * lim(x->2) (x-2)/sin(x-2)

∵ x->2时,t=(x-2）->0 ,lim(x->2) (x-2)/sin(x-2)=lim(t->0) t/sint = 1

= 4*1

=4