Solutions for the Mathematics section of the quiz


```python
import sympy as sym
import nash
import pulp

sym.init_printing()
```

Question 1.


```python
x = sym.symbols('x')
sym.integrate(sym.exp(x) * sym.cos(x))
```

Question 2.


```python
sym.limit((x ** 4 - 1) / (x ** 2 - 1), x, 1)
```

Question 3.


```python
M = sym.Matrix([[0, sym.S(1) / 2, sym.S(1) / 2], 
                [sym.S(1) / 2, 0, sym.S(1) / 2],
                [0, 0, 1]])
pi = sym.Matrix([[0, 0, 1]])
pi * M
```

Question 4.


```python
prob = pulp.LpProblem("2017_quiz", pulp.LpMinimize)
x = pulp.LpVariable("x", lowBound=0)
y = pulp.LpVariable("y", lowBound=0)
prob += 4 * x + 12 * y
prob += 5 * x - y >= 2
prob += x + 2 * y <= 1
prob.solve()
```


```python
x.value(), y.value()
```


```python
2 / 5
```

297cba7a525ad28473131c68ded89700607d8c48
ipynb
Jupyter Notebook
main.ipynb
drvinceknight/quiz
3bec0c11918d795027f4fa2f12502372f6bc3e59
MIT
main.ipynb
drvinceknight/quiz
3bec0c11918d795027f4fa2f12502372f6bc3e59
MIT
main.ipynb
drvinceknight/quiz
3bec0c11918d795027f4fa2f12502372f6bc3e59
MIT
Qwen/Qwen-72B
1. YES
2. YES