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112年 - 臺灣綜合大學系統112 學年度學士班轉學生聯合招生考試試題 微積分A#120563
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5. Find the radius of convergence and interval of convergence of the power series
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其他申論題
1. Evaluate the limit.
#513632
2. Find the point on the curve y = that is closest to the point (1,0).
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3. If f(x) =
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4. Find the length of the polar curve r = sin³(θ/3), 0 ≤ θ ≤ π.
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6. Find the unit tangent vector and the unit normal vector for the curve r(t) = cos 3t i + sin 3t j + 4t k.
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7. Find equations of the tangent plane and the normal line to the surface x+2y+3z = sin(xyz) at the point (2,-1,0).
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8. Evaluate the integral
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9. Evaluate ∫c F ⋅ dr, where F = and C is the unit circle x² + y² = 1.
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10. Evaluate ∬s F ⋅ dS, where F(x,y,z) =+ (x²y + cosh z)j + (y²z + x)k and S is the top half of sphere x² + y² + z² = 1.
#513641
一、申論題秋水時至,百川灌河,涇流之大,兩涣渚崖之間,不辯牛馬。於是焉河伯欣然自喜,以天下之美為盡在己。順流而東行,至於北海,東面而視,不見水端,於是焉河伯始旋其面目,望洋向若而歎,曰:「野語有之曰『聞道百,以為莫己若』者,我之謂也。且夫我嘗聞少仲尼之聞而輕伯夷之義者,始吾弗信,今我睹子之難窮也,吾非至於子之門則殆矣,吾長見笑於大方之家。」《莊子·秋水》 請依據上文內容,說明該段文字主旨。
#513642
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