作业帮 > 数学 > 作业

①求极限lim (x→0) (sin kx)/x=?

来源:学生作业帮 编辑:神马作文网作业帮 分类:数学作业 时间:2024/11/18 19:19:13
①求极限lim (x→0) (sin kx)/x=?
②求∫(cos√ x)/√ x d(x)=?
①求极限lim (x→0) (sin kx)/x=?
(1)lim (x→0) (sin kx)/x
=lim (x→0) k(sin kx)/(kx)
=k*lim (x→0) (sin kx)/(kx)
=k*1
=k
(2)令√ x=t dx=dt^2=2tdt
∫(cos√ x)/√ x d(x)
=∫cost/t*2tdt
=∫2costdt
=2∫costdt
=2sint+C
=2sin√ x+C (其中C为常数)