2. (20 pts) In this problem, we will graph f(z) = - + In(1). a) First, compute the limit lim a In(x). You'll need this later. b) Determine if the function f(x) has a vertical asymptote at = = 0. Hint: Rewrite the given function as a quotient. Then use the work from part (a) when you computed the limit lim rIn(x). c) Find all local extrema of f, and the intervals on which f is increasing and decreasing. Make sure to identify each local extremum as a maximum or minimum. d) Find all inflection points of f, and the intervals on which f is concave up and concave down. e) Determine if f(x) has any horizontal asymptotes. f) Use the information that you obtained in parts (a)-(e) to sketch the graph of f on its domain. . You should clearly label all local extrema and inflection points. . You do NOT need to determine the exact y-values of inflection points (just a rough approximation is fine)