(1) sin2x 5x sin2x 2
lim -------------------=lim--------------*lim------------ *------ =2/5
x→0 sin 5x x→0 sin 5x x→0 2x 5
(2) arctanx (arctanx)' 1/(1+x²)
lim -------------=lim ------------------ =lim-----------------=1
x→0 x x→0 (x)' x→0 1
(1) sin2x 5x sin2x 2
lim -------------------=lim--------------*lim------------ *------ =2/5
x→0 sin 5x x→0 sin 5x x→0 2x 5
(2) arctanx (arctanx)' 1/(1+x²)
lim -------------=lim ------------------ =lim-----------------=1
x→0 x x→0 (x)' x→0 1