Question

求极限：x→0时(sin3x-sinx)/x

Answer 1

解法一：等价无穷小 lim sinx/sin3x x→0 =lim x/(3x) x→0 =⅓ 解法二：洛必达法则 lim sinx/sin3xx→0 =lim cosx/(3cos3x) x→0 =cos0/(3·cos0) =1/(3·1) =⅓

Answer 2

原式=[3(sin3x)/(3x)]-[(sinx)/x]
当x--->0时，3x--->0
∴(sin3x)/(3x)--->1
(sinx)/x--->1
∴原式--->3×1-1=2