** code the following using only sympy commands

For each of the following functions, find values a and b such that, on interval [a, b], the Inter- mediate Value Theorem holds, proving the function has at least one real root on that interval.

Graph the function on the interval to visualize your result. Finally, use Python to find the root on the given interval. (a) f(x) = 100e

x/100 0.01x 2 (b) g(x) = arctan(x) + x 1 (c) h(x) = ln(x) x + 100 x 2 (Hint: Note the domain of this function)

2. For each of the following functions, find values a and b such that, on interval [a,b], the Intermediate Value Theorem holds, proving the function has at least one real root on that interval. Graph the function on the interval to visualize your result. Finally, use Python to find the root on the given interval. (a) f(x)=100ex/1000.01x2 (b) g(x)=arctan(x)+x1 (c) h(x)=ln(x)x+100x2 (Hint: Note the domain of this function)