110年 - 110 國立嘉義大學_碩士班(甲組)招生考試試題_應用數學系：微積分#146593

1. Find the derivative of
2
2
31
3
x
y
x
 − =   + . (10%)

2. Determine the slope of the graph of ( )
2 22 3 100 x y xy += at the point (3,1). (10%)

3. Evaluate
1
0
arcsin( ) x dx ∫ . (10%)

4. Find the volume of the solid formed by revolving the region bounded by the graphs
of 2
yx y x x =+ = = = 1, 0, 0 and 1 about the y-axis. (10%)

5. Find ( ) 0
lim sin x
x
x → + . (10%)

6. Find the area of the region bounded by the graphs 2 fx x () 2 = − and gx x () = . (10%)

7. Determine the convergence or divergence of the series
2
1
n
n
n
e
n
∞
=
∑ . (10%)

8. Find the indefinite integral 2 16 4 − x dx ∫ . (10%)

9. Find the arc length of the graph of the function
3
6
1
2
x
y
x
= + over the interval
1 ,2
2

 . (10%)

10. Determine the convergence or divergence of the series
1
( 1)
ln( 1)
n
n
n
n
∞
=
−
+ ∑ . (10%)