Q. 0 - Calculus

Question

 Read the sections and make your own summary of the material.

 

Step-by-Step Solution

Answer

Ans:  Summary of this chapter:

The infinite limit $\underset{x\to c}{lim} f\left(x\right)=\mathrm{\infty }$ means that for all M > 0, there exists δ > 0 such that

       if $x\in (c-\delta ,c)\cup (c,c+\delta ),\text{ then }f\left(x\right)\in (M,\mathrm{\infty })$.

The limit at infinity $\underset{x\to \mathrm{\infty }}{lim} f\left(x\right)=L$ means that for all  $\in$> 0, there exists N > 0 such

that

            if $x\in (N,\mathrm{\infty }),\text{ then }f\left(x\right)\in (L-ϵ,L+ϵ)$.

The infinite limit at infinity $\underset{x\to \mathrm{\infty }}{lim} f\left(x\right)=\mathrm{\infty }$ means that for all M > 0, there exists

N > 0 such that

           if $x\in (N,\mathrm{\infty })\text{, then }f\left(x\right)\in (M,\mathrm{\infty })$.

Step 1. Given information.

given,

      Read the sections and make your own summary of the material.

Step 2. Limits Involving Infinity:

The infinite limit$\underset{x\to c}{lim} f\left(x\right)=\mathrm{\infty }$ means that for all M > 0, there exists δ > 0 such that

       if $x\in (c-\delta ,c)\cup (c,c+\delta ),\text{ then }f\left(x\right)\in (M,\mathrm{\infty })$.

The limit at infinity $\underset{x\to \mathrm{\infty }}{lim} f\left(x\right)=L$ means that for all  $\in$> 0, there exists N > 0 such

that

            if $x\in (N,\mathrm{\infty }),\text{ then }f\left(x\right)\in (L-ϵ,L+ϵ)$.

The infinite limit at infinity l$\underset{x\to \mathrm{\infty }}{lim} f\left(x\right)=\mathrm{\infty }$ means that for all M > 0, there exists

N > 0 such that

           if $x\in (N,\mathrm{\infty })\text{, then }f\left(x\right)\in (M,\mathrm{\infty })$.