```python
import sympy as sm
```

# Limit
> ## $ \lim \limits_{x \to \pi} sin(\frac{x}{2}+sin(x))$


```python
x = sm.symbols('x')
expr = sm.sin(x/2 + sm.sin(x))
sm.limit(expr,x,sm.pi)
```




$\displaystyle 1$



## $ \lim \limits_{x\to0^{+}} \frac{2e^{1/x}}{e^{1/x}+1} $


```python
sm.limit(2*sm.exp(1/x) / (sm.exp(1/x)+1),x,0,dir='+')
```




$\displaystyle 2$



## $ \lim\limits_{x \to \infty} \frac{cos(x)-1}{x}$


```python
sm.limit( (sm.cos(x)-1)/x, x, sm.oo)
```




$\displaystyle 0$



# Derivatvies
## $ \frac{d}{dx}(\frac{1+sin\,x}{1-cos\, x})^2 $


```python

```

2b3f8af6cf62c8e58565b05a7e3c44b64938ceb6
ipynb
Jupyter Notebook
python/Vectors/limits.ipynb
karng87/nasm_game
a97fdb09459efffc561d2122058c348c93f1dc87
MIT
python/Vectors/limits.ipynb
karng87/nasm_game
a97fdb09459efffc561d2122058c348c93f1dc87
MIT
python/Vectors/limits.ipynb
karng87/nasm_game
a97fdb09459efffc561d2122058c348c93f1dc87
MIT
Qwen/Qwen-72B
1. YES
2. YES