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題組內容

7. The Bessel function of order 0 is defined by , answer the following questions:

(a) Find the domain of by the Ratio Test.

其他申論題

3. Find the velocity and acceleration vectors for the position vector

4. Symbolically find δ in terms of ε for

5. Find the Maclaurin series of and its interval of convergence. Also, use it to determine the value of

6. Find a vector function that represents the curve of intersection of the cylinder x² + y² = 4 and the plane y+z=2 with parameter t. Also, find the arc length of the intersection curve for 0≤t≤π.

(b) Show that satisfies the differential equation: , where and are the second and first derivative of , respectively.

(c) Evaluate the first 3 terms of without calculating the number.

II. 計算證明題: 1. Find the right circular cylinder of maximum volume that can be inscribed in a sphere of radius 10 centimeters.

2. Show that the surface area of a sphere of radiusr is 4πr2.

一、請以塞尚的油畫作品為例,分析他的畫面組合方式與效果。

二、通常我們看作品時會說這作品很有觀念性,請以一件作品為例解釋所謂觀念性指的是甚麼。

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