Q. 0 - Calculus

Question

Read the section and make your own summary of material.

Step-by-Step Solution

Answer

The section describes the Limit, Limit at infinite, Infinite limit, Infinite limit at infinite, Left-hand limit, Right-hand limit, and vertical and horizontal asymptote of function.

Step 1. Given information.

The given chapter name is An Intuitive Introduction to Limits.

Step 2. Summary.

Notation for Limits.

Limit:$\underset{x\to c}{\lim }f\left(x\right)=L$

Limit at infinite: $\underset{x\to \infty }{\lim }f\left(x\right)=L$

Infinite limit: $\underset{x\to c}{\lim }f\left(x\right)=\infty$

Infinite limit at infinite: $\underset{x\to \infty }{\lim }f\left(x\right)=\infty$

Left-hand limit:$\underset{x\to c^{-}}{\lim }f\left(x\right)=L$

Right-hand limit: $\underset{x\to c^{+}}{\lim }f\left(x\right)=R$

A function has a vertical asymptote at $x=c$for the following conditions.

$$\begin{gathered} \underset{x\to c^{+}}{\lim }f\left(x\right)=\infty \\ \underset{x\to c^{-}}{\lim }f\left(x\right)=\infty \\ \underset{x\to c^{+}}{\lim }f\left(x\right)=-\infty \\ \underset{x\to c-}{\lim }f\left(x\right)=-\infty \end{gathered}$$

A function has a horizontal asymptote at $y=L$for the following conditions.

$$\begin{gathered} \underset{x\to \infty }{\lim }f\left(x\right)=L \\ \underset{x\to -\infty }{\lim }f\left(x\right)=L \end{gathered}$$