4.3.7-Suppose f(x) less than g(x). If lim_{x \to c} f(x)=\infty, then lim_{x \to c} g(x)=infty. скачать в хорошем качестве

4.3.7-Suppose f(x) less than g(x). If lim_{x \to c} f(x)=\infty, then lim_{x \to c} g(x)=infty.

4.3.7 Let $A \subseteq \mathbb{R}$, let $f, g : A \to \mathbb{R}$, and let $c \in \mathbb{R}$ be a cluster point of $A$. Suppose that $f(x) \leq g(x)$ for all $x \in A$, $x
eq c$. a) If $\displaystyle \lim_{x \to c} f(x) = \infty$, then $\displaystyle \lim_{x \to c} g(x) = \infty$. b) If $\displaystyle \lim_{x \to c} g(x) = -\infty$, then $\displaystyle \lim_{x \to c} f(x) = -\infty$. \textbf{(UQ Oct 2019)} This video is based on the topic 4.3.7 (Infinite Limits) of the syllabus of Mathematical Analysis for V Semester B.Sc. Mathematics (for affiliated colleges under Mahatma Gandhi University) Text Book: Introduction to Real Analysis (Third Edition) Author: Robert G. Bartle, Donald R. Sherbert