高数问题只有高悬赏才有高手来解，高！实在是高！

x趋向于0时
f(x)=3cos x-sin(3x)
=3cos0-sin(3x0)
=3

不是无穷小，楼主题目有问题啊

楼主的题目应该是 f(x)=3cos x-sin(3x)/x 吧

f(x)=3cos x - sin(3x)/x
=[3xcos x-sin(3x)] / x

只看分子3xcos x-sin(3x)
设g(x)=3xcos x-sin(3x)
g'(x)=3cosx-3xsinx-3cosx
=-3xsinx
-3xsinx与-3x^2为等价无穷小
即g'(x)与-3x^2为等价无穷小
所以g(x)与-x^3为等价无穷小
g(x)/x与-x^2为等价无穷小
g(x)/x即为f(x)

即f(x)与-x^2为等价无穷小

所以c=-1 k=2