Q. 0 - Calculus

Question

Read the section and make your own sum-

mary of the material.

Step-by-Step Solution

Answer

 Section Infinite Limits and Indeterminate Forms state the Limits Whose Denominators Approach Zero from the Right or the Left, Whose Denominators Become Infinite Approach Zero, Limits of Some Basic Functions at Infinity, and horizontal asymptote of a rational function.

Step 1. Given information.

 The given topic of the section is Infinite Limits and Indeterminate Forms. 

Step 2. Summary of section.

• Limits Whose Denominators Approach Zero from the Right or the Left.
  If the limit $\underset{x\to c}{\lim }\frac{f\left(x\right)}{g\left(x\right)}$is in the form of $\frac{1}{0^{\pm }},$then $\underset{x\to c}{\lim }\frac{f\left(x\right)}{g\left(x\right)} =\pm \infty .$
• Limits Whose Denominators Become Infinite Approach Zero.
  If the limit $\underset{x\to c}{\lim }\frac{f\left(x\right)}{g\left(x\right)}$is in the form of $\frac{1}{\pm \infty }$then $\underset{x\to c}{\lim }\frac{f\left(x\right)}{g\left(x\right)} =0.$
• Limits of Some Basic Functions at Infinity.$$\begin{gathered} \underset{x\to \infty }{\lim }{x}^k=\infty \& \underset{x\to \infty }{\lim }{x}^{-k}=0, \mathrm{where} k>0. \\ \underset{x\to \infty }{\lim }{e}^{kx}=\infty \& \underset{x\to \infty }{\lim }{e}^{-kx}=0, \mathrm{where} k>0. \\ \underset{x\to \infty }{\lim }\ln x=\infty \end{gathered}$$
  Limits of $\sin \left(x\right),\cos \left(x\right),\tan \left(x\right),sec\left(x\right),csc\left(x\right), \& cot\left(x\right)$as $x\to \infty$do not exist.
• If in rational function $\frac{p\left(x\right)}{q\left(x\right)},$polynomials $p\left(x\right) \& q\left(x\right)$have the leading term $a_n{x}^n \& b_m{x}^m$ respectively then,
  Graph of function have horizontal asymptote at $y=0$when $n<m.$
  Graph of function have horizontal asymptote at $y=\frac{a_n}{b_m}$when $n=m.$
  Graph of function do not have horizontal asymptote when $n>m.$