Let h be the function given by h(x) = x^5 + x - 2/x^2 - 1. What is the domain of h? Explain why lim_x rightarrow 1 x^5 + x - 2/x^2 - 1 results in an indeterminate form. Next we will investigate the behavior of both the numerator and denominator of h near the point where x = 1. Let f(x) = x^5 + x - 2 and g(x) = x^2 - 1. Find the local linearizations of f and g at a = 1, and call these functions L_f(x) and L_g(x), respectively. Explain why h(x) L_f(x)/L_g(x) for x near a = 1. Using your work from (c) and (d), evaluate lim_x rightarrow 1 L_f(x)/L_g(x). What do you think your result tells us about lim_x rightarrow 1 h(x)? Investigate the function h(x) graphically and numerically near x = 1. What do you think is the value of lim_x rightarrow 1 h(x)?