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1.O Ž.

(a)lim x →0x 2

sin 3

2tdt

x 0

t (t −sin t )dt

.

)‰.

ª=lim x →02x sin 3

2x 2

x (x −sin x )

=lim x →02x 4

x ·x 3

6=12.

(b) arctan √xdx..

)‰.

ª=x arctan √x − 11+x ·12x −1

2·xdx

=x arctan √x −12 x 12

1+x dx =x arctan √x − y

1+y 2·ydy y =√x

=x arctan √x −y +arctan y +C

=(x +1)arctan √x −√x +C.

(c)2 1dx x

√x 1y e −x dy +4 2dx 2

√x 1y e −

x dy.