Initial program 57.9
\[\frac{e^{x} - e^{-x}}{2}\]
Taylor expanded around 0 0.6
\[\leadsto \frac{\color{blue}{2 \cdot x + \left(\frac{1}{3} \cdot {x}^{3} + \frac{1}{60} \cdot {x}^{5}\right)}}{2}\]
Simplified0.6
\[\leadsto \frac{\color{blue}{{x}^{5} \cdot \frac{1}{60} + x \cdot \left(x \cdot \left(\frac{1}{3} \cdot x\right) + 2\right)}}{2}\]
- Using strategy
rm Applied distribute-rgt-in0.6
\[\leadsto \frac{{x}^{5} \cdot \frac{1}{60} + \color{blue}{\left(\left(x \cdot \left(\frac{1}{3} \cdot x\right)\right) \cdot x + 2 \cdot x\right)}}{2}\]
Final simplification0.6
\[\leadsto \frac{{x}^{5} \cdot \frac{1}{60} + \left(2 \cdot x + \left(x \cdot \left(\frac{1}{3} \cdot x\right)\right) \cdot x\right)}{2}\]
