5.3 The Fundamental Theorem of Calculus: Difference between revisions
Jump to navigation
Jump to search
No edit summary |
No edit summary |
||
| Line 2: | Line 2: | ||
* [https://youtu.be/4wtY6o87BuE Link] | * [https://youtu.be/4wtY6o87BuE Link] | ||
== Lecture notes == | |||
:1. FTC #1 <math>\int_{a(x))^(b(x))=</math><br> | |||
: <math>x</math> is called the <b>input</b> or <b>argument</b> of the function and <math>f(x)</math> or <math>y</math> is called the <b>output</b> or <b>value</b> at <math>x</math> | |||
:: ex. If <math>f(x)=x^2+x+1</math> what is the value of <math>f</math> at <math>x=3</math>? | |||
:: The value of <math>f</math> at <math>x=3 \text{ is } 13</math> | |||
:2. <math>(x, y) \text{ or } (x, f(x)) </math> is called an <b>ordered pair</b> where <math>x</math> is the input and <math>y \text{ or } f(x)</math> is the output | |||
Revision as of 16:32, 23 August 2022
Lecture
Lecture notes
- 1. FTC #1 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \int_{a(x))^(b(x))=}
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle x}
is called the input or argument of the function and or is called the output or value at Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle x}
- ex. If Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle f(x)=x^2+x+1} what is the value of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle f} at Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle x=3} ?
- The value of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle f} at Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle x=3 \text{ is } 13}
- 2. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle (x, y) \text{ or } (x, f(x)) } is called an ordered pair where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle x} is the input and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle y \text{ or } f(x)} is the output