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Suppose that $f$ and $g$ are two functions such that$$\lim _{x \rightarrow a} g(x)=0 \quad \text { and } \quad \lim _{x \rightarrow a} \frac{f(x)}{g(x)}$$$$\text { exists. Use Theorem } 1.2 .2 \text { to prove that } \lim _{x \rightarrow a} f(x)=0$$

$\lim _{x \rightarrow a} g(x)=0$

Calculus 1 / AB

Chapter 1

LIMITS AND CONTINUITY

Section 2

Computing Limits

Functions

Limits

Continuous Functions

Harvey Mudd College

University of Nottingham

Boston College

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

01:30

Suppose that $f$ and $g$ a…

00:55

02:34

Show that if both $$\lim _…

00:54

Proof Prove that if $f(x) …

01:11

Find two functions $f(x)$ …

02:20

$$\begin{aligned}&…

01:53

01:00

04:50

Prove that if $$\lim _{x \…

02:56

Finding Functions Find two…

broken in number 48. Ah, limits. Oh, extremes to a oh, every backs is a flirt, too. Living extends to 80 Oh, f of X over you rex times gox. So my theory, Mom going toe to be another weight right back that way. So since limits of extends to zero g off X is equal to zero. So here we can say that it is a 1 to 0. Um, so which is what we want to show that the limits here. Any limits. What going boy? You should be, But with you, which what we want to show.

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In mathematics, precalculus is the study of functions (as opposed to calculu…

In mathematics, a function (or map) f from a set X to a set Y is a rule whic…

Suppose that $f$ and $g$ are two functions such that both$\lim _{x \righ…

Suppose that $f$ and $g$ are two functions such that$\lim _{x \rightarro…

Show that if both $$\lim _{x \rightarrow c} f(x) g(x)$$ and $$\lim _{x \righ…

Proof Prove that if $f(x) \geq 0, \quad \lim _{x \rightarrow a} f(x)=0, \qua…

Find two functions $f(x)$ and $g(x)$ with the given properties.$$\lim _{…

$$\begin{aligned}&\text { Proof of Limit Law 2 Suppose } \lim f(x)=L…

Prove that if $$\lim _{x \rightarrow c} f(x)$$ exists and $$\lim _{x \righta…

Finding Functions Find two functions $f$ and $g$ such that $$\lim _{x \right…

01:12

Evaluate the limit using an appropriate substitution.$$\lim _{x \rig…

03:14

The given limit represents $f^{\prime}(a)$ for some function $f$ and some nu…

01:02

Find the limits.$$\lim _{x \rightarrow 2^{+}} \frac{1}{|2-x|}$$<…

02:26

Let$$f(x)=\left\{\begin{array}{cl}{x-1,} & {x \leq 3} \\ {3 x-7,…

02:29

(a) Explain why the following argument is incorrect.$$\begin{aligned…

04:35

A function $y=f(x)$ and values of $x_{0}$ and $x_{1}$ are given.(a) Find…

03:25

In each part determine whether the function is continuous or not, and explai…

00:30

Determine whether the statement is true or false. Explain your answer.$$…

01:57

Use Formula ( 12 ) to find $d y / d x$$y=\frac{1}{x+1}$

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