Numbers

See

• [[ analysis/foundations/Complex Numbers ]]
• Series
• Permutations
• Euler’s Number

Exercises

1. Find the domain of functions $\frac{x-3}{x-2}$, $\frac{x+1}{x^2-3x+2}$, $\sqrt{x-2}$, $\sqrt{

   x-2

   }$, etc.

2. Analyze piecewise-defined functions, determine if they are monotone and/or bounded.

3. Determine the composition $f_1 \circ f_2$ and $f_2 \circ f_1$, where $f_1(x) = \frac{x-3}{x-2}$ and $f_2(x) =

   x-5

   $.

4. For a given piecewise function, compute one-sided limits at discontinuity points.