5.4.1
Euler's Method visualized with mapping diagram and graph, showing
the connection for the Fundamental Theorem of Calculus between the mapping diagram and estimating
$$\int_a^b P(x)dx = f(b) - f(a)$$ where $f'(x) = P(x)$
x | f(x) | f'(x) | df=f'(x)dx |
0. | 0 | 1.0 | 0.2 |
0.2 | 0.2 | 1.4 | 0.28 |
0.4 | 0.48 | 1.8 | 0.36 |
0.6 | 0.84 | 2.2 | 0.44 |
0.8 | 1.28 | 2.6 | 0.52 |
1.0 | 1.80 | 3.0 | 0.60 |
1.2 | 2.40 | 3.4 | 0.68 |
1.4 | 3.08 | 3.8 | 0.76 |
1.6 | 3.84 | 4.2 | 0.84 |
1.8 | 4.68 | 4.6 | 0.92 |
2.0 | 5.60 |
|
|
|
![](data:image/png;base64,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) |
![](data:image/png;base64,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) |
Move the sliders to change $a,b$, and $N$. You can also change the
function $P(x) = f'(x)$ by entering a new function in the box.
In context of the Sensible Calculus Text: IV.F
Euler's Method Meets The Position,
Cost, and Area Problem
5.4.2 Euler's Method visualized with mapping diagram and graph, showing
the connection for the Fundamental Theorem of Calculus between the mapping diagram and
$$\int_a^b P(x)dx $$ where $f'(x) = P(x)$ evaluated by GeoGebra's CAS. ¤
Move the sliders to change $a,b$, and $N$. You can also change the
function $P(x) = f'(x)$ by entering a new function in the box.
6 & 7.Sequences and Series