Question

求数学帝一位,函数极限问题当X趋近于1时 分子为 TAN[X-1].分母为X的平方减去一 .等于多少呢

Answer 1

1【罗必塔法则】

lim(x->1) tan(x-1)/(x^2-1)

=lim(x->1) [ 1/cox(x-1)^2 ]/2x

= 1/2

2【等价无穷小量代换】

x->1 时,t = x-1 -> 0

t->0 时,tant t --> tan(x-1) (x-1)

lim(x->1) tan(x-1)/(x^2-1)

=lim(x->1) (x-1)/(x^2-1)

=lim(x->1) 1/(x+1)

= 1/2