Riemann surface
matlab
还在面临预备微积分的学习挑战吗？别担心！我们的calculus-primer-guide团队专业为您解决函数、极限、导数等方面的问题。我们拥有深厚的专业背景和丰富的经验，能帮您完成高水平的作业和论文，让您的学习之路一帆风顺！
以下是一些我们可以帮助您解决的问题：
函数和图像：函数的定义、性质和分类，函数的图像和性态分析，如奇偶性、周期性等。
极限和连续性：极限的概念、性质和计算方法，函数的连续性和间断点的分类，如可导性和间断点的判定。
导数和微分：导数的定义和计算方法，函数的导数和微分的性质，如导数的运算规则、高阶导数等。
积分和面积：定积分和不定积分的概念、性质和计算方法，曲线下面积的计算，如积分的换元法、分部积分等。
微分方程：常微分方程的概念、基本类型和求解方法，如一阶微分方程、二阶线性微分方程等。
应用问题：微积分在物理学、经济学、工程学等领域的应用，如速度、加速度、优化问题等。
无论您面临的预备微积分问题是什么，我们都会尽力为您提供专业的帮助，确保您的学习之旅顺利无阻！
From 1990 through 2003, the amounts $A$ (in millions of dollars) spent on skiing equipment in the United States are shown in the table, where $t$ represents the year. Sketch a scatter plot of the data. (Source: National Sporting Goods Association)
Solution
To sketch a scatter plot of the data shown in the table, you simply represent each pair of values by an ordered pair $(t, A)$ and plot the resulting points, as shown in Figure 4. For instance, the first pair of values is represented by the ordered pair $(1990,475)$. Note that the break in the $t$-axis indicates that the numbers between 0 and 1990 have been omitted.
Find the distance between the points $(-2,1)$ and $(3,4)$.
Algebraic Solution
Let $\left(x_1, y_1\right)=(-2,1)$ and $\left(x_2, y_2\right)=(3,4)$. Then apply the Distance Formula.
$$
\begin{aligned}
d & =\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2} & & \text { Distance Formula } \
& =\sqrt{[3-(-2)]^2+(4-1)^2} & & \begin{array}{l}
\text { Substitute for } \
x_1, y_1, x_2 \text {, and } y_2 \text { – }
\end{array} \
& =\sqrt{(5)^2+(3)^2} & & \text { Simplify. } \
& =\sqrt{34} & & \text { Simplify. } \
& \approx 5.83 & & \text { Usc a calculator. }
\end{aligned}
$$
So, the distance between the points is about 5.83 units. You can use the Pythagorean Theorem to check that the distance is correct.
$$
\begin{aligned}
d^2 & \stackrel{?}{=} 3^2+5^2 \
(\sqrt{34})^2 & \stackrel{?}{=} 3^2+5^2 \
34 & =34
\end{aligned}
$$
Pythagorean Theorem
Substitute for $d$.
Distance checks.
E-mail: help-assignment@gmail.com 微信:shuxuejun
help-assignment™是一个服务全球中国留学生的专业代写公司
专注提供稳定可靠的北美、澳洲、英国代写服务
专注于数学，统计，金融，经济，计算机科学，物理的作业代写服务