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Algebra IAlgebra IWelcome Welcome to Central
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Algebra IAlgebra IWelcomeWelcome to Central
This wiki has been created to help students understand the criteria that CollegeBoard has for the AP Calculus exams. If you are interested in contributing to the wiki, feel free to contact me at sacampbell@shenandoah.k12.va.us.
Feel free to browse the following areas:

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Algebra IAlgebra IWelcome to
This wiki has been created to help students understand the criter…

Algebra IAlgebra IWelcome to
This wiki has been created to help students understand the criteria that CollegeBoard has for the AP Calculus exams. If you are interested in contributing to the wiki, feel free to contact me at sacampbell@shenandoah.k12.va.us.
Feel free to browse the following areas:

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edited
Welcome Algebra IWelcome to Central
This wiki has been created to help students understand th…

WelcomeAlgebra IWelcome to Central
This wiki has been created to help students understand the criteria that CollegeBoard has for the AP Calculus exams. If you are interested in contributing to the wiki, feel free to contact me at sacampbell@shenandoah.k12.va.us.
Feel free to browse the following areas:
AP Calculus
Algebra I SOL

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... Welcome to Central Math Teacher
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...

Welcome to Central Math Teacher
This wiki has been created to help students understand the criteria that CollegeBoard has for the AP Calculus exams. If you are interested in contributing to the wiki, feel free to contact me at sacampbell@shenandoah.k12.va.us.
Feel free to browse the following areas:
AP Calculus

*ε represents a small positive number
*δ represents a positive number Changed by Mr. Campbell
Larson, Hosteler, Edward, Calculus Eighth Edition
example an intuitive understanding of the limit process

*ε represents a small positive number
*δ represents a positive number
Changed by Mr. Campbell
Larson, Hosteler, Edward, Calculus Eighth Edition
example an intuitive understanding of the limit process

the term e^{-.02t} approaches
$
e^{-.02t}
approaches 0 thus
Question is from "In preperation for the AP calculus (AB) Exam, Sample Exam VI, Section 2 Part B, #5

You can prove that f is continuous at x=c by showing that f(x) approaches f(c) as x moves toward c. To do this, use the differentiability of f at x=c and consider the following limit.
$
\lim_{\ x\toc}f(x)-f(c)=\lim{\x\toc}\frac{(x-c)(f(x)-f(c)}{(x-c)}=0x\to c}f(x)-f(c)=\lim{\x\toc}\frac{(x-c)(f(x)-f(c)}{(x-c)}=0
Because the difference of f(x)-f(c) comes to zero as x approaches c, you know that the lim as x approaches c of f(x)=f(c). Therefore , f is continuous at x=c.
To sum up the relationship between continuity and differentiability: