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研究所、轉學考(插大)-微積分
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102年 - 102 國立暨南大學轉學生招生考試試題_資工系二、土木系二、應化系二、電機系、應光系二：微積分#124233
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題組內容
4. (20%) Evaluate the following integrals
(a) (10%)∫sin
5
x dx.
其他申論題
(a) (5%) Describe the mean-value theorem.
#528157
(b) (10%) Use the mean-value theorem to show that 10 + ＜＜ 10 +[Hint: Consider f(x) = on(1000, 1150)]
#528158
2. (10%) Sketch the graph of the functionf(x) = (x3 -x2 - 6x + 2), x∈ [-2, -∞).
#528159
3. (10%) Find[Hint: limit of Riemann sums]
#528160
(b) (10%).
#528162
5. (10%) We know that the region below the graph of $f(x) =, x≥1 has infinite area. Show that the volume of the solid generated by revolving the region about the x-axis is equal to π.
#528163
6. (10%) Verify that the series has interval of convergence [-1, 1].
#528164
7. (10%) For , evaluate the limit as (x, y) approaches the origin along the line y = mx.
#528165
(a) (5%) Find the gradient ∇f(x,y), where f(x,y) = 4x2 + y2.
#528166
(b) (10%) Determine the path of steepest descent along the surface f(x, y) = 4x2 + y2 from the point (2, 1, 17).
#528167
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