---
# System prepended metadata

title: Some Techniques
tags: [Calculus]

---

# Some Techniques
###### tags: `Calculus`
## Limit of f(x) contain [x]
$$
for\;those\;f(x)\;contain\;\lbrack x\rbrack\\We\;can\;find\;the\;limit\;by\;knowing\;x-1<\lbrack x\rbrack\leq x\;\\and\;use\;Squeeze\;Thm\;to\;find\;the\;limit
$$
## Note!!
$$
if\;encounter\;\sqrt{x^2}\;remember\;to\;change\;it\;into\;\left|x\right|\;instead\;of\;x\;itself
$$
## Derivative of inverse function
$$
Since\;we\;know\;f(f^{-1}(x))=x\\By\;chain\;rule\;we\;can\;know\;f'(f^{-1}(x))\cdot\frac d{dx}f^{-1}(x)=1\\\Rightarrow\frac d{dx}f^{-1}(x)=\frac1{f'(f^{-1}(x))}
$$
