# 微积分网课代修|积分学代写Integral Calculus代考|MTH252 Continuous at a point

• 单变量微积分
• 多变量微积分
• 傅里叶级数
• 黎曼积分
• ODE
• 微分学

## 微积分作业代写calclulus代考|Continuous at a point.

DEFinition 3.8. A function $F: \mathbb{R} \rightarrow \mathbb{R}$ is continuous at a point $x_{0}$ if $F$ does not grow on the set $E=\left{x_{0}\right}$.

EXERCISE 31. Show that a function $F: \mathbb{R} \rightarrow \mathbb{R}$ is continuous at a point $x_{0}$ if and only if for every $\epsilon>0$ there is a $\delta>0$ so that $\left|F\left(x_{0}\right)-F(x)\right|<\epsilon$ whenever $\left|x-x_{0}\right|<\delta$.

## 微积分作业代写calclulus代考|Continuous function

A function is continuous if it is continuous at every point.

DEFinition 3.9. A function $F: \mathbb{R} \rightarrow \mathbb{R}$ is continuous if $F$ does not grow on any singleton set $E=\left{x_{0}\right}$.

EXERCISE 32. Show that a function is continuous if and only if it does not grow on any finite set.
SOLUTION IN SECTION 8.3.5.
EXERCISE 33. Show that a function is continuous if and only if it does not grow on any set $E$ whose elements can be written as a sequence $E=\left{e_{1}, e_{2}, e_{3}, \ldots\right}$.
SOLUTION IN SECTION ??

## 微积分作业代写calclulus代考| Continuous at a point.

$\mathrm{E}=\left{\right.$ left $\left{\mathrm{x}{\mathbf{\prime}}{0} \mid\right.$ right $}$. 练习 31.显示函数 $F: \mathbb{R} \rightarrow \mathbb{R}$ 在某一点上是连续的 $x{0}$ 当且仅当 $\epsilon>0$ 有一个 $\delta>0$ 因 此 $\left|F\left(x_{0}\right)-F(x)\right|<\epsilon$ 每当 $\left|x-x_{0}\right|<\delta$.

## 微积分作业代写calclulus代考| Continuous function

$\mathrm{E}=\left\langle\right.$ left $\left{\mathrm{x}{\mathbf{\prime}{\mathrm{O}}} \backslash \text { right }}}\right.$. 练习 32. 证明一个函数是连续的，当且仅当它不在任何有限集合上增长。 解决方案在第 $8.3 .5$ 节中。 练习 33.显示函数是连续的，当且仅当它不在任何集合上增长 $E$ 其元素可以写成序列 $\mathrm{E}=\left\langle\right.$ left $\left{\mathrm{e}{2}{1}\right.$ ， e_{2}， e_{3}， |Idots|right $}$.