In this question, we will evaluate the limit 1077 x 1 lim x-1 x (a) Is the function x1077 1 x- 1 continuous at x = 1? What does that mean for computing the limit? The function is not continuous at x=1, so the limit automatically does not exist. (b) Make the substitution h = = x - 1. What happens to the limit? 1077 х - lim x+1 x- 1 1 = lim lim(h→0) ((h+1)^1077 - 1)/h h→0 (c) Your limit in (b) looks a lot like a derivative. Find a function f(x) and a constant a so that your limit above computes f'(a). Then, using derivative rules, evaluate the limit. lim x→1 1077 x - x-1 - 1 = = f'(a) = 1 The numbers involved in this problem are not completely precise (since the exact numbers are randomized), but the ranges are set up to be fairly accurate for 2024. In other words, your final answer is pretty close to the real-world answer. Suppose the national debt of the United States of America is currently 35.3 trillion dollars, and currently increasing at a rate of 8 billion dollars a day. Suppose also the population of the USA is currently 347 million, and is currently increasing at a rate of 1.1 million people per year. (You can find updated values with a quick internet search). Given this information, at what rate is the national debt per capita currently changing? Give your answer in terms of dollars (per person) per day. Current rate of change of national debt per capita is dollars per day.