Differentiation
Definition 5.1.1 Let $I\subset \mathbb{R}$ be an interval and let $f:I\rightarrow\mathbb{R}$ be a function. Fix a $p\in I$. The derivative of $f$ at $p$ is ...
Recent posts
Monotone Functions and Discontinuities
Definition 4.4.1 $E\subset \mathbb{R}, f:E\to\mathbb{R}, p$ is a limit point of $E\cap (p,\infty)$. $f$ has a right limit at $p$ if there exists a $L\in\math...
Uniform Continuity
Definition 4.3.1 Let $E$ be a subset of $\mathbb{R}$ and let $f:E\to\mathbb{R}$ be a function. The function $f$ is uniformly continuous on $E$ if $\forall ...
Continuous functions-(2)
Lemma 1
Continuous functions-(1)
Definition 4.2.1 $f:E\to \mathbb{R}$ is continuous at $p\in E$, if $\forall \epsilon >0, \exists \delta >0$ such that $|x-p|<\delta \Rightarrow |f(...