# 应用经济|ECON10162T Applied Economics代写 manchester代写

For completeness, we define an approximate integral that is also a linear spline, with a breakpoint sequence $z_{i+1}=\left(\nu_{i}+\nu_{i+1}\right) / 2$ for $i=2, \ldots, n$ and with additional break points defined by extrapolating beyond the original sequence: $z_{1}=\left(3 \nu_{1}-\nu_{2}\right) / 2$ and $z_{n+1}=\left(3 \nu_{n}-\nu_{n-1}\right) / 2$. The approximation to the integral,
$$F(x)=\int_{\nu_{1}}^{x} f(x) d x$$
at the new breakpoints is
$$F\left(z_{i}\right)=F\left(z_{i-1}\right)+\left(z_{i}-z_{i-1}\right) f\left(\nu_{i-1}\right),$$
where
$$F\left(z_{1}\right)=\frac{1}{2}\left(\nu_{1}-\nu_{2}\right) f\left(\nu_{1}\right)$$

(this ensures the normalization that $\left.F\left(\nu_{1}\right)=0\right) .{ }^{3}$ This definition produces an approximation to the integral at the original breakpoints that is equal to the approximation obt ained by applying the trapezoid rule :
$$\int_{\nu_{i}}^{\nu_{i+1}} f(x) d x \approx \frac{1}{2}\left(\nu_{i+1}-\nu_{i}\right)\left(f\left(\nu_{i+1}\right)+f\left(\nu_{i}\right)\right) .$$
(we leave the verification of this assertion as exercise for the reader).

myassignments-help数学代考价格说明

1、客户需提供物理代考的网址，相关账户，以及课程名称，Textbook等相关资料~客服会根据作业数量和持续时间给您定价~使收费透明，让您清楚的知道您的钱花在什么地方。

2、数学代写一般每篇报价约为600—1000rmb，费用根据持续时间、周作业量、成绩要求有所浮动(持续时间越长约便宜、周作业量越多约贵、成绩要求越高越贵)，报价后价格觉得合适，可以先付一周的款，我们帮你试做，满意后再继续，遇到Fail全额退款。

3、myassignments-help公司所有MATH作业代写服务支持付半款，全款，周付款，周付款一方面方便大家查阅自己的分数，一方面也方便大家资金周转，注意:每周固定周一时先预付下周的定金，不付定金不予继续做。物理代写一次性付清打9.5折。

Math作业代写、数学代写常见问题

myassignments-help擅长领域包含但不是全部: