alvierahman90/notes
1
1
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity

more consistent use of details/summary

Browse Source
This commit is contained in:
Akbar Rahman 2021-12-02 16:33:31 +00:00
parent dc1cd6f8ff
commit ef91ba0126
Signed by: alvierahman90
GPG Key ID: 20609519444A1269
1 changed files with 15 additions and 0 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

15
mechanical/mmme1026_maths_for_engineering/calculus.md
View File

@ -40,6 +40,9 @@ Its range has to exclude all those values of $x$ where $g(x) = 0$.
</details> </details>
<details>
<summary>
### Inverse Functions ### Inverse Functions
Consider the function $f(x) = y$. Consider the function $f(x) = y$.
@ -48,6 +51,12 @@ we can define the inverse $f^{-1}$ as:
$$f^{-1}(y) = f^{-1}(f(x)) = x$$ $$f^{-1}(y) = f^{-1}(f(x)) = x$$
</summary>
</details>
<details>
<summary>
### Limits ### Limits
Consider the following: Consider the following:
@ -64,6 +73,8 @@ $$\lim_{x \rightarrow a} f(x)$$
to be the limiting value, if it exists, of $f(x)$ as $x$ gets approaches $a$. to be the limiting value, if it exists, of $f(x)$ as $x$ gets approaches $a$.
</summary>
#### Limits from Above and Below #### Limits from Above and Below
Sometimes approaching 0 with small positive values of $x$ gives you a different limit from Sometimes approaching 0 with small positive values of $x$ gives you a different limit from
@ -79,12 +90,16 @@ $$\lim_{x \rightarrow a^-} f(x)$$
If the two limits are equal, we simply refer to the *limit*. If the two limits are equal, we simply refer to the *limit*.
</details>
## Important Functions ## Important Functions
### Exponential Function ### Exponential Function
$$f(x) = e^x = \exp x$$ $$f(x) = e^x = \exp x$$
<details> <details>
<summary> <summary>
It can also be written as an infinite series: It can also be written as an infinite series: