[methods] finalise exponential/log notes

diff --git a/methods/graphics/exponential-graphs.png b/methods/graphics/exponential-graphs.png
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diff --git a/methods/graphics/log-graphs.png b/methods/graphics/log-graphs.png
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diff --git a/methods/stuff.md b/methods/stuff.md
index cd3aeb07cb8360d595a11befb075a6ab35e1f681..2055b63a7d86e0fb419e1f9b851304547ead4d5b 100644 (file)
--- a/methods/stuff.md
+++ b/methods/stuff.md
@@ -1,5 +1,5 @@
 ---
 ---

-geometry: margin=2cm
+geometry: margin=1.5cm

 <!-- columns: 2 -->
 graphics: yes
 tables: yes
 <!-- columns: 2 -->
 graphics: yes
 tables: yes


@@ -41,7 +41,6 @@ If $a<1, \quad \log_{b} a < 0$ (flip inequality operator)
 
 $e^x$ - natural exponential function
 
 
 $e^x$ - natural exponential function
 

-

 $$\lim_{h \rightarrow 0} {{e^h-1} \over h}=1$$
 
 ## Logarithm laws
 $$\lim_{h \rightarrow 0} {{e^h-1} \over h}=1$$
 
 ## Logarithm laws


@@ -65,10 +64,6 @@ $$f^{-1}: \mathbb{R}^+ \rightarrow \mathbb{R}, f^{-1}=log_ax$$
 
 $$e= \lim_{n \rightarrow \infty} (1 + {1 \over n})^n$$
 
 
 $$e= \lim_{n \rightarrow \infty} (1 + {1 \over n})^n$$
 

-## Literal equations
-
-_Literal equation_ - no numerical solutions
-

 ## Exponential and logarithmic modelling
 
 $$A = A_0 e^{kt}$$
 ## Exponential and logarithmic modelling
 
 $$A = A_0 e^{kt}$$


@@ -91,9 +86,11 @@ $$f(x)=Aa^{k(x-b)} + c, \quad \vert \> a > 1$$
 - dilation of factor $A$ from $x$-axis
 - dilation of factor $1 \over k$ from $y$-axis
 
 - dilation of factor $A$ from $x$-axis
 - dilation of factor $1 \over k$ from $y$-axis
 

+![](graphics/exponential-graphs.png){#id .class width=30%} 
+

 ## Graphing logarithmic functions
 
 ## Graphing logarithmic functions
 

-$log_e x$ is the inverse of $e^x$ (reflection across $y=x$)
+$\log_e x$ is the inverse of $e^x$ (reflection across $y=x$)

 
 $$f(x)=A \log_a k(x-b) + c$$
 
 
 $$f(x)=A \log_a k(x-b) + c$$
 


@@ -106,6 +103,8 @@ where
 - dilation of factor $A$ from $x$-axis
 - dilation of factor $1 \over k$ from $y$-axis
 
 - dilation of factor $A$ from $x$-axis
 - dilation of factor $1 \over k$ from $y$-axis
 

+![](graphics/log-graphs.png){#id .class width=30%} 
+

 ## Finding equations
 
 Solve simultaneous equations on CAS: ![](graphics/cas-simultaneous.png){#id .class width=75px}
 ## Finding equations
 
 Solve simultaneous equations on CAS: ![](graphics/cas-simultaneous.png){#id .class width=75px}

diff --git a/methods/stuff.pdf b/methods/stuff.pdf
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