💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Like

Report

Get the answer to your homework problem.

Try Numerade Free for 7 Days

A curve has equation $ y = f(x) $. (a) Write an expression for the slope of the secant line through the points $ P(3, f(3)) $ and $ Q(x, f(x)) $.(b) Write an expression for the slope of the tangent line at $ P $.

a) $m=\frac{f(x)-f(3)}{x-3}$b) $\lim _{x \rightarrow 3} \frac{f(x)-f(3)}{x-3}$

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 7

Derivatives and Rates of Change

Limits

Derivatives

Daniel N.

July 12, 2021

Suppose that f(x) is a function and that for any given ? > 0, the condition 0 < |x ? 2| < 3 4 ? guarantees that |f(x) ? 5| < ?. (a) What limit is described by this statement?

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

Boston College

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

02:23

Use the method in Example …

03:00

04:06

Find the slope of the tang…

01:11

Find an equation of the ta…

03:39

a. Use definition ( 2 ) ( …

01:10

13:35

02:50

04:31

Equations of tangent lines…

00:59

Find an equation of the cu…

This is problem number one of the Stuart Calculus eighth edition section two point seven a curve as equation y equals FX party or an expression for the slope of the Secret Line through the points P, which is three, comma half of three. And Q, which is X comma ethics. Let's recall the equation of a slope em is equal to change of. Why over change, Becks, which is the same as if you have two points. Why two minus want one over X to my six one. So for this problem, our first point x one by one his Pene, our second point thanks to Y two is Kyu. So why to is aftereffects why one is three ex to his ex and x one is three. So this is our expression for the slope of the signalling. Through the point, Pete and Q pervy are an expression for the slope of the tangent line at P. And every CP is at the point X equals three. So, in fact, what we do is we use what we know about party and by definition, the slope of its tangent line at Pete is exactly this function as X approaches three. So as Ex gets closer and closer to three, and for this we write a limit as X approaches. Three of this same function, the same expression after Lex, myself of three, divided by ex ministry. And that is the expression for the slope of the tension line, people.

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…

Use the method in Example 3 to find (a) the slope of the curve at the given …

Find the slope of the tangent line to each curve when $x$ has the given valu…

Find an equation of the tangent line to$$f(x)=3^{x}$$

a. Use definition ( 2 ) ( $p .$ 135 ) to find the slope of the line tangent …

Equations of tangent lines by definition ( 2 )a. Use definition (2) (p. …

Find an equation of the curve whose tangent line has a slope of$f^{\prim…