USE PYTHON

4. Given f(x) = 1 tan(x) sin(x) cos(x) :

a) Graph f(x) on the interval [0, 1]. Use the graph to estimate lim x/4 f(x).

b) Use list comprehension to evaluate the function at x = 0.78, 0.785, 0.7853, then at x = 0.79, 0.786, 0.7854 to numerically estimate lim x/4 f(x) and lim x/4+ f(x).

c) Find the exact limit.

d) To see how to evaluate the limit algebraically, substitute sin(x) cos(x) for tan(x) in f, then simplify the result (print both).