Question

高数题 求讲解！！

高数题 求讲解！！步骤没看懂 为啥分完0正和0负前面那个分数也不一样

Answer 1

等价无穷小
lim (x-sinxcos2x)/cx^k=1
分子分母同为0
洛必达法则
=lim [1-(cosxcos2x-2sinxsin2x)]/ckx^(k-1)
=lim -(-sinxcos2x-2cosxsin2x-2cosxsin2x-4sinxcos2x)/ck(k-1)x^(k-2)
=lim (5sinxcos2x+4cosxsin2x)/ck(k-1)x^(k-2)
=lim (5cosxcos2x-10sinxsin2x-4sinxsin2x+8cosxcos2x)/ck(k-1)(k-2)x^(k-3)
此时分子不为0，所以k-3=0
k=3
原式
=13/6c=1
c=6/13