Limits from graph In this problem we evaluate limits from the graph. Consider the graph of f given in [Figure 1]. Evaluate each of the following limits (or explain why if the limit does not exist). a) { lim_(x -> -1) f(x) } b) { lim (x -> 2) f(x) c) { lim (x-> 0^+ ) f(x) } Figure A. Diagram for Optimization Problem Math 192 Final Exam, Problem 20 fix) 2 Figure 1. Graph of f(x) Math 192 Final Exam, Problem 1 QUESTION 20 Optimization A corral with three separate regions is constructed against a river as indicated in the diagram below. The amount of fence material available is 48,000 ft. Find the dimensions that will maximize the total area enclosed (and also this total area) | { river Please also see [Figure A] for a better representation. Give the objective and constraint equations. Reduce the objective to one variable and use the derivative to maximize. flt) *2 -1 2 Figure 2. Graph of f(t) Math 192 Final Exam, Problem 23 2. QUESTION 23 accumulated area This problem deals with the graph of f(t) given in [Figure 2] We look at the accumulated area beneath this curve, as in the definite integral as follows F(x) f(t) dt -2 { F(x) = int_(-2)^x f(t) dt a) Use ordinary area formulas to compute each of the following: F(-1), F(0), F(3) and F(5) b) Find the value of F(3) - F(0), and sketch the corresponding area on the graph. BONUS(2): Sketch on the graph the area corresponding to F(2+h) - F(2), where h represents some small (positive) quantity.