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110年 - 110 國立中山大學碩士暨碩士專班招生考試_應數系碩士班/乙組:微積分#104294
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8. (10 %) Find the volume of the solid inside both x
2
+ y
2
+ z
2
= 36 and (x - 3)
2
+ y
2
= 9.
其他申論題
(a) (5%) Findxdx
#441525
(b) (10 %) Evaluate the improper integral
#441526
6. (10 %) State the Integral Test and apply it to determine the convergence or divergence of the series:
#441527
7. (20 %) Find the length of r = 1 + cos θ and area of its interior region.
#441528
9. (10 %) Use the change of variables to evaluate the given double integral where R is the region given in the picture on the right.
#441530
1.解下列微分反應方程式:(15%)
#441531
2.試求下列函數之拉普拉斯轉換:(15%)
#441532
(1)溫度梯度(∇T)(5%)
#441533
(2)於點(1,-1,2)之溫度梯度(5%)
#441534
(3)於點(1,-1,2)沿著p=2i+2j-k方向的方向導數(directional derviv)(5%)
#441535
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