设f(x)=sinax/x在x=0处连续,f(0)=-1/2(负的).则a=()A.2B.-2C.-1/2D.1/2

Question

设f(x)=sinax/x在x=0处连续,f(0)=- 1/2(负的).则a=( )
A.2
B.-2
C.- 1/2
D.1/2

Answer 1

当x=0时,f(x)的分子,分母都为0
利用洛必达法则求极限,上下求导
=acosax/1=a=-1/2
所以a=-1/2
选C