Summary: A Calculus Problem Revisited,
or: On Beyond Varberg
Problem 37 From §5.4 of Varberg et al. Calculus, 9th ed
CAS Using the same axes, draw the graphs of y = xn on [0, 1] for
n = 1, 2, 4, 10 and 100. Find the length of each of these curves.
Guess at the length when n = 10, 000.
Graphs of the powers of x
Figure: y = xn
for n = 1, 2, 4, 10, 100.
As the exponent n
gets larger, the
graph of y = xn
"flat" and "steep"
The red dot shows
Length of y = xn