Objective of the project is to use technology to find the arc length of a curve using simulations and simple programming concept and compare it with the theoretical results.
Question 1: Consider the curve:
$y = \frac{1}{3}x^3 + \frac{1}{4x}, x \ge 1$
1) Graph the curve provided above.
2) Find the arc length function for this curve starting with the point $x \ge 1$.
3) Graph the arc length function.
4) On the same figure, graph the function provided as well as the arc length function.
5) Write your observation about the obtained result.
Question 2: Consider the curves of fat circles given by the equation:
$x^n + y^n = 1$, $n = 4, 6, 8, ...$
1) Graph the curves with $n = 4, 6, 8, 10, 12$ to see why it is called fat circle.
2) Set up an integral for the length of the fat circle $L_n$ where $n$ is an even number.
3) Without attempting to evaluate this integral. State the value of $\lim_{n \to \infty} L_n$
Notes about graphing:
1) You can use Matlab, wxMaxima, Maple, symbolab graphing calculator to graph the curves.
2) Label the axes and provide a caption to each graph.
3) Provide legends when needed.
