Question

极限练习题2请写出步骤和方法.

Answer 1

用等价无穷小代换或者洛必达法则都容易.

1.等价无穷小代换：

=lim{x-->0}sin5x/3x-lim{x-->0}tanx/3x

=lim{x-->0}5x/3x-lim{x-->0}x/3x

=5/3-1/3

=4/3

2.洛必达法则

=lim{x-->0}(5cos5x-sec^2x)/[(3/(1+3x)]

=(5-1)/3

=4/3.