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研究所、轉學考(插大)-微積分
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95年 - 95 國立臺灣師範大學_轉學生招生考試試題_資訊工程學系二年級：微積分#122368
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題組內容
4. (12 pts)Find
(a)
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其他申論題
8. Let R be the annular region lying between the two circles x² + y² = 1 and x² + y² = 5, as shown in Figure 1. Evaluate the integral (x² + y²) dA. (15 分)
#521177
1. (12 pts)Find the Taylor series generated by f(x)=1/x at a=3. Where, if anywhere, does the series converge to 1/x?
#521178
2. (10 pts)Evaluate ∫excosx dx.
#521179
3. (12 pts)Find the solution to dy/dx = 2xy(y²+1) that satisfies y(0) = 1.
#521180
(b)
#521182
(c).
#521183
(a) ;
#521184
(b).
#521185
6. (12 pts)The usual way to evaluate the improper integral I = dx is first to calculate its square: I² = dxdy. Evaluate the integral and solve the resulting equation for I.
#521186
7. (10 pts)Find the values of ∂z/∂x and ∂z/∂y at point (x,y,z)=(1, 1, 1) and z³ - xy + yz + y³ - 2 = 0.
#521187
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