Question

当lim x→∏时怎么证明 sin3x/sin2x=?

Answer 1

sin3x=sin(3∏-3x),

当lim x→∏时,3∏-3x→0,则sin(3∏-3x)与3∏-3x是等价无穷小.

同理,sin2x= -sin(2∏-2x),

当lim x→∏时,2∏-2x→0,则sin(2∏-2x)与2∏-2x是等价无穷小.

则原式=lim(x→0) sin(3∏-3x)/(-sin(2∏-2x) )

=3(∏-x)/(-2·(∏-x))

= -3/2