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1/2 week 1 notes

by: Melissa Newell

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1/2 week 1 notes MAC 2311

Melissa Newell
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syllabus fyi 2.1, 2.2 and 2.3
COURSE
Calculus I
PROF.
Vincent Naudot
TYPE
Class Notes
PAGES
2
WORDS
KARMA
Free

Popular in Applied Mathematics

This 2 page Class Notes was uploaded by Melissa Newell on Friday August 19, 2016. The Class Notes belongs to MAC 2311 at Florida Atlantic University taught by Vincent Naudot in Fall 2016. Since its upload, it has received 7 views. For similar materials see Calculus I in Applied Mathematics at Florida Atlantic University.

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Date Created: 08/19/16
Calculus I first day notes  Syllabus  ● The syllabus is online  ● Everything regarding the course can be read on the syllabus  ● Can only find homework through the syllabus  ○ math.fau.edu/naudot/c1/c1.htm  ○ Quiz 1 covers 2.1­> 2.4 (August 29)  FYI  ● Homework is not collected but th​ uizzes and exams  ​ are randomly chosen from the  homeworks    Background Material  ● Chapter 1 (review on own time)  ● (a+b)^2 = a^2 + 2ab + b^2  ● (a+b)^3 = a^3+3a^2b+3ab^2+b^3  ● speed= distance traveled/time spent  ○ f(t)= position of a point on a horizontal line    Lecture 2.1­2.3  ● Limits  ○ Form  ■ lim   f(x)  x­>a        =    L  ■  Which can be understood that limit of f(x) is equal to L as x leads to a if  f(x) approaches L as x approaches a     ● x does not equal a  ■ When ​ ​f(x) is a polynomial (x)     ● lim  poly(x)  x­>a           =    poly(a)  ○ Graphs  ■ A nonvertical line admits the equation​ y=Δ​x + ​   ● Δ is the slope  ● β is the y­intercept   ● Slope of a Secant line  ○ [f(t2) ­ f(t1)] / [t2 ­ t1]      ● Slope of a tangent line  ○ lim    [f(a +h) ­ f(a)]  ­­­­­­­­­­­­­­­­­  h­>0           h  Big Brother   ● Theorem 2.3 [page 70 in textbook]  ○ Rule 1  ■ lim [f(x)+g(x)] lim f(x) lim  g(x)  x­>a = x­>a + x­>a  ○ Rule 2  ■ lim δ[​(x)] δ ​im  [​(x)]  x­>a =    x­>a  ○ Rule 3  ■ lim  f(x)  *  lim g(x) lim    [f(x)*g(x)]  x­>a       x­>a = x­>a  ○ Rule 4  ■ lim [f(x)/g(x)] lim    f(x)  x­>a x­>a  = ­­­­­­­­­­­­­­­­­­­  lim    g(x)  x­>a  ● But a requirement lim g(x) cannot equal zero when x approaches  a  ○ Rule 5  ■   Homework   ● Find the tangent lines  ○ f(x)= x^2 +4x at x=1  ○ f(x)= x^3 at x=1  ○ f(x)=(x)^½ at x=1

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