Backlinks
- lrm;lrm;
Table of Contents
1 Rate of Change (1, chemical reaction)
- Average rate of change (slope) between \(t=20\) and \(t=30\) is \(0.615\)
- \(f\left(x\right)\ =\ \frac{\left(A_{0}\left(1-\exp\left(-k\left(x+p\right)\right)\right)-A_{0}\left(1-\exp\left(-k\left(x\right)\right)\right)\right)}{p}\)
- Show that it looks like the tangent at \(x=25\): \(y=f\left(25\right)\left(x-25\right)+51.444\)
- Desmos Graph
2 Rate of Change (2, washing machines)
- Average cost for \(100\) machines = \(\frac{11000}{100} = 110\)
- Derivative is \(y = -0.2x + 100\), so we get \(80\)
- By hard coding the numbers, we get \(\left(2000+100\cdot101-0.1\left(101\right)^{2}\right)-\left(\left(2000+100\cdot100-0.1\left(100\right)^{2}\right)\right) = 79.9\) which is roughly \(80\)
- Demos Graph
3 Terminology
(slide 13 is confusing, see questions.*)*
4 Limits
- Eq \(\frac{x^3-1}{x-1} \Rightarrow \{x^2+x+1 : x \neq 1\}\)
4.1 Limits Practice
- \(\lim_{x\to 10}2x+5 = 25\)
- \(\lim_{x\to -2} \frac{x^2-x-6}{x-2} = -5\)
- \(\lim_{x\to 4} \frac{x-4}{\sqrt{x}-2} \Rightarrow *\frac{\sqrt{x}+2}{\sqrt{x}+2} \Rightarrow \sqrt{x}+2 = 4\)
- \(\lim_{x\to 0} \frac{sin x}{x}\): \(sin x = x\) for small \(x\) (SHM), so we can treat it like \(\frac{x}{x}\) #todo
- \(\lim_{x\to 0} sin\frac{1}{x}\) Keeps changing… Not sure how to evaluate. #todo
- \(\lim_{x\to 2}\lfloor x \rfloor\)