Question

lim当x趋近于1时，怎么求极限？

Answer 1

举例说明：lim(x^2+ax+b)/sin(x^2-1)
分母当x→1时极限是0,故分子极限也应为0,否则最后结果不可能是常数.即1^2+a*1+b=a+b+1=0,解得b=-a-1
原式=lim(x^2+ax+b)/(x^2-1)(等价无穷小代换)
=lim(x^2+ax-a-1)/(x^2-1)
=lim[(x^2-1)+a(x-1)]/(x^2-1)
=1+alim(x-1)/(x^2-1)
=1+alim1/(x+1)
=1+a/2=3