作业 3(单元的 10%)
• 您提交的内容可以是手写的,但必须清晰可辨。
• 必须清楚地显示得出答案的所有步骤(工作)。 可以使用讲座中讨论的所有公式 – 否则必须导出结果。
• 只有(扫描的)电子提交将通过单位网站(Deakin Sync)被接受。
• 您提交的内容必须是一个pdf 文件。 多个文件和/或不同的文件格式,例如 .jpg,将不被接受。
• 标有* 的问题是较难的问题。

1. 计算以下极限 lim e2x −1−2x,x→0 x2
2. 评估以下积分
(i) ?x(x−6) dx
(二)? 1 dx x2 + 9
(三)? −3x + 23 dx x2 +x−12(2 分)
23 1/2
3. 求曲线 y = (1 − 2x) 下方和 x 轴上方的正 x 轴上的面积绕 x 轴旋转时形成的体积。(2 分)

4. 求解下列微分方程。 (A)
(b) dy = xy; y(0)=3 dx
dy+2y=x; y(1)=2 dx x
5.判断下列数列收敛还是发散?∞ n 3 n=1 e2n

6. (a) 使用已建立的麦克劳林级数找到 f(x) = e−x2/2 的前三个非零项
(b) 使用你在 (a) 中的表达式求出?ax2e−x2/2 dx,0(4 marks)(2 marks) 的近似值,前提是 a 在收敛区间内。 将你的近似表示为 a 的函数。
7. *计算不定积分 ? (sin−1 x)2dx(4 分)(4 分)


SIT194: Introduction To Mathematical Modelling
Assignment 3 (10% of unit)
Due date: 11:00pm AEST Thursday, 12 September 2019
Important notes:
• Your submission can be handwritten but it must be legible.
• All steps (workings) to arrive at the answer must be clearly shown. All formula discussed in lectures can be used – otherwise results must be derived.
• Only (scanned) electronic submission would be accepted via the unit site (Deakin Sync).
• Your submission must be in ONE pdf file. Multiple files and/or in different file format, e.g. .jpg, will NOT be accepted.
• Question marked with a * are harder questions.

1. Evaluate the following limit lim e2x −1−2x,x→0 x2
2. Evaluate the following integrals
(i) ?x(x−6) dx
(ii) ? 1 dx x2 + 9
(iii) ? −3x + 23 dx x2 +x−12(2 marks)
23 1/2
3. Find the volume formed when the area, on the positive x-axis that is below the curve y = (1 − 2x) and above the x-axis, is rotated about the x axis.(2 marks)
(6 marks)

4. Solve the following differential equations. (a)
(b) dy =xy; y(0)=3 dx
dy+2y=x; y(1)=2 dx x
5. Determine whether the following series converges or diverges?∞ n 3 n=1 e2n

6. (a) Use established MacLaurin series to find the first three non-zero terms of f(x) = e−x2/2
(b) Use your expression in (a) to find an approximation of?ax2e−x2/2 dx,0(4 marks)(2 marks) provided a is within the interval of convergence. Express your approximation as a func- tion of a.
7. *Evaluate the indefinite integral ? (sin−1 x)2dx(4 marks)(4 marks)

以上就是关于SIT194 Mathematical Modelling Assignment 3的数学建模代写作业相关内容,如果需要该作业代写需要的可以随时跟我们客服咨询。