\(\left(\left(x \cdot a\right) \cdot \left(x \cdot a\right)\right) \cdot \left(\frac{1}{2} + x \cdot \left(\frac{1}{6} \cdot a\right)\right) + x \cdot a\)
- Started with
\[e^{a \cdot x} - 1\]
48.3
- Applied taylor to get
\[e^{a \cdot x} - 1 \leadsto \frac{1}{2} \cdot \left({a}^2 \cdot {x}^2\right) + \left(\frac{1}{6} \cdot \left({a}^{3} \cdot {x}^{3}\right) + a \cdot x\right)\]
21.4
- Taylor expanded around 0 to get
\[\color{red}{\frac{1}{2} \cdot \left({a}^2 \cdot {x}^2\right) + \left(\frac{1}{6} \cdot \left({a}^{3} \cdot {x}^{3}\right) + a \cdot x\right)} \leadsto \color{blue}{\frac{1}{2} \cdot \left({a}^2 \cdot {x}^2\right) + \left(\frac{1}{6} \cdot \left({a}^{3} \cdot {x}^{3}\right) + a \cdot x\right)}\]
21.4
- Applied simplify to get
\[\color{red}{\frac{1}{2} \cdot \left({a}^2 \cdot {x}^2\right) + \left(\frac{1}{6} \cdot \left({a}^{3} \cdot {x}^{3}\right) + a \cdot x\right)} \leadsto \color{blue}{\frac{1}{2} \cdot {\left(x \cdot a\right)}^2 + \left(x \cdot a + \left(\frac{1}{6} \cdot {a}^3\right) \cdot {x}^3\right)}\]
21.4
- Using strategy
rm 21.4
- Applied add-cbrt-cube to get
\[\frac{1}{2} \cdot {\left(x \cdot a\right)}^2 + \left(x \cdot a + \color{red}{\left(\frac{1}{6} \cdot {a}^3\right) \cdot {x}^3}\right) \leadsto \frac{1}{2} \cdot {\left(x \cdot a\right)}^2 + \left(x \cdot a + \color{blue}{\sqrt[3]{{\left(\left(\frac{1}{6} \cdot {a}^3\right) \cdot {x}^3\right)}^3}}\right)\]
23.4
- Applied simplify to get
\[\frac{1}{2} \cdot {\left(x \cdot a\right)}^2 + \left(x \cdot a + \sqrt[3]{\color{red}{{\left(\left(\frac{1}{6} \cdot {a}^3\right) \cdot {x}^3\right)}^3}}\right) \leadsto \frac{1}{2} \cdot {\left(x \cdot a\right)}^2 + \left(x \cdot a + \sqrt[3]{\color{blue}{{\left(\frac{1}{6} \cdot {\left(a \cdot x\right)}^3\right)}^3}}\right)\]
9.0
- Applied taylor to get
\[\frac{1}{2} \cdot {\left(x \cdot a\right)}^2 + \left(x \cdot a + \sqrt[3]{{\left(\frac{1}{6} \cdot {\left(a \cdot x\right)}^3\right)}^3}\right) \leadsto \frac{1}{2} \cdot \left({a}^2 \cdot {x}^2\right) + \left(x \cdot a + \sqrt[3]{{\left(\frac{1}{6} \cdot {\left(a \cdot x\right)}^3\right)}^3}\right)\]
17.9
- Taylor expanded around inf to get
\[\frac{1}{2} \cdot \color{red}{\left({a}^2 \cdot {x}^2\right)} + \left(x \cdot a + \sqrt[3]{{\left(\frac{1}{6} \cdot {\left(a \cdot x\right)}^3\right)}^3}\right) \leadsto \frac{1}{2} \cdot \color{blue}{\left({a}^2 \cdot {x}^2\right)} + \left(x \cdot a + \sqrt[3]{{\left(\frac{1}{6} \cdot {\left(a \cdot x\right)}^3\right)}^3}\right)\]
17.9
- Applied simplify to get
\[\color{red}{\frac{1}{2} \cdot \left({a}^2 \cdot {x}^2\right) + \left(x \cdot a + \sqrt[3]{{\left(\frac{1}{6} \cdot {\left(a \cdot x\right)}^3\right)}^3}\right)} \leadsto \color{blue}{\left(\left(x \cdot a\right) \cdot \left(x \cdot a\right)\right) \cdot \left(\frac{1}{2} + x \cdot \left(\frac{1}{6} \cdot a\right)\right) + x \cdot a}\]
0.2
