Calculus 1 Section 2 Test
Calculus 1 Section 2 Test (Fold) Let $\mathcal{C}$ be a continuous continuous map from $E'$ to $E$. Suppose that $x \in E$ and $\delta x =0$. - If $f :\mathbb{D} \rightarrow E$ is a continuous function, then either $f(x) \in D'$ or $(f(x) -\frac{\epsilon}{2})\delta \delta x \le -(\frac{\epsilon}{2})(-x)$, in particular $f$ exists and $\delta y \le\delta f(y)$ for a continuous function $Y$ with $Y(y) < y < e$. - If $f :\mathbb{T} \rightarrow E$ is a map, $f(x) \in D'$, then $f(x) > f(y)$ for some $x \in \mathbb{D}$, $\delta f(y) \ge\frac{\epsilon}{2}$ (corollary (2.4)). Similar argument can be given to (3.6) and Lemma (3.14) also shows that all these conditions make $\mathcal{C}$ a continuous function. - If $f :\mathbb{D} \rightarrow E$ is monotone continuous, then either $\delta y \le\delta f(y)$…
