This project examines the exponential function fx xx Execut

This project examines the exponential function f(x) = x^x. Execute the command \"plot (x^x, x = -1 ... 1);\". Why does Maple give a partial plot? (It is reasonable to hope that if x_1 x_2, then f(x_1) f(x_2). Find, if possible, f (-1/10) and f(-1/11).) Isa point at x = 0 plotted? Evaluate f(0). Can you find (or estimate)lim_x rightarrow 0^+ f(x)? Estimate the value of each expression and then evaluate using Maple: f(0.1), f(0.01), f(-1), f(-0.5), f(-0.4), f(-1/3), f(-1/4). Explain the appearance of complex numbers (containing 1) in some of these results.

Solution

x^x will have imaginary part not equal to zero if x is negative

limit of f(x) x going to zero from positive side is 1.