With n = 10
The following steps should help you to figure out what happens to the Hill function hn(x) = xn / l + xn for large values of n.
a. Compute the value of the function at x = 0, x = 1, and x = 2.
b. Compute the derivative and evaluate at x = 0, x = 1, and x = 2.
c. Sketch a graph.
d. hn(x) can be thought of as representing a response to a stimulus of strength x. Would the response work as a good filter, giving a small output for inputs less than 1 and a large output for inputs greater than 1 ?