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

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?

3. (12 pts)Find the solution to dy/dx = 2xy(y²+1) that satisfies y(0) = 1.

(a);

(b)

(c).

(a) ;

(b).

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.

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.

8. (10 pts)Find the tangent and normal to the curve x³ + y³ - 9xy = 0 at point (2, 4).

9. (12 pts)Find the horizontal tangents to the graph of the cardioid r=1-cosθ, 0 ≤ θ ≤ 2π. (That is, find the points at which horizontal lines tangent to the curve.)

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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