所屬科目：研究所、轉學考(插大)-微積分
1.Please prove the derivative of Sine function by the limit definition of the derivative. (10 分)[sin x] / dx = cos x
2. Find the tangent line to the graph given by x²(x² + y²) = y² at the point (), as shown in Figure 1. (15 分)
(a)-ax2 dx, a>0
(b)dx, a>0
4. Evaluate dx. (10 分)
6. Evaluate dx. (15 分)
7. Find the curvature of the parabola given by y = x -x² at x = 2, and sketch the circle of curvature at (2, 1). (15 分)
8.** Let R be the region bounded by the square with vertices (0, 1), (1, 2), (2, 1), (1, 0). Evaluate the integral ((x + y)²sin²(x - y)) dA. (15 分)
阿摩線上測驗
登入
阿摩線上測驗
登入
[sin x] / dx = cos x
), as shown in Figure 1. (15 分)
-ax2 dx, a>0 
dx, a>0
dx. (10 分)
dx. (15 分)
x² at x = 2, and sketch the circle of curvature at (2, 1). (15 分)
((x + y)²sin²(x - y)) dA. (15 分)