Plot the graph of x^y = y^x in the first quadrant and explain its properties.
Investigate the graphs of y = [1 + (x - t)^2][1 + (x + t^)2] as the parameter t varies.
Sketch the graphs of y = sin x and y = tan x and some straight lines. Prove some inequalities.
Given probabilities of taking paths in a graph from each node, use matrix multiplication to find the probability of going from one vertex to another in 2 stages, or 3, or 4 or even 100.