# SymPy


```python
import sympy as sp
import numpy as np
import matplotlib.pyplot as plt
```


```python
x = sp.symbols('x')
sp.init_printing()
```

---

$$ \Large 
{\displaystyle f(x)=3e^{-{\frac {x^{2}}{8}}}} \sin(x/3)
$$

&nbsp;

$$\Large 
{\displaystyle g(x)=\frac{1}{5}x^{3} + \frac{1}{2}x^{2} + \frac{1}{3}x - \frac{1}{2}}
$$

---

## Show that:

$$ \Large
\left.{\frac {d}{dx}\, f(x)}\ \right|_{\ x\, =\, 0}\ = \ \left.{\frac {d^{2}}{dx^{2}}\, g(x)}\ \right|_{\ x\, =\, 0}
$$


```python

```


```python

```


```python

```


```python

```

## Plot $f(x)$ and $g(x)$ on the same plot over the interval $[-4 \le x \le 2]$


```python

```


```python

```


```python

```


```python

```

## What are the value(s) for $x$ where $f(x)\ = \ g(x)$


```python

```


```python

```


```python

```

---
### Due Wed Mar 2 - 1 pm
- `File -> Download as -> HTML (.html)`
- `upload your .html file to the class Canvas page`


```python

```

c432305fbc7db9396ad4f9a770993edb43084829
ipynb
Jupyter Notebook
HW_Sympy.ipynb
UWashington-Astro300/Astro300-W22
371eb704030a104cb8e826bb14c353e5a863b0f3
MIT
HW_Sympy.ipynb
UWashington-Astro300/Astro300-W22
371eb704030a104cb8e826bb14c353e5a863b0f3
MIT
HW_Sympy.ipynb
UWashington-Astro300/Astro300-W22
371eb704030a104cb8e826bb14c353e5a863b0f3
MIT
Qwen/Qwen-72B
1. YES
2. YES