Question

①求极限lim (x→0) (sin kx)/x=?

Answer 1

(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）