전체 글102 [Notes & HW Answers] 4.5 Applications to Marginality [Prepwork 4.5] Q1. What is the relationship between (total) cost and marginal cost? A: Marginal cost is the derivative of total cost Q2. Suppose C and R are the cost and revenue functions for a particular product. Check all the statements below that are true. A. The critical points of the profit function happen when 𝑀𝑅=𝑀𝐶 or one of these derivatives does not exist. B. The profit is maximized whe.. 2022. 12. 6. [Notes & HW Answers] 4.4 Families of Functions and Modeling 2022. 12. 6. [Notes & HW Answers] 4.3 Optimization and Modeling [Prepwork 4.3] Q1. Consider the following problem: You are standing on a river bank and want to get to a house that is on the other side of the river and 800 feet up the river as quickly as possible. The river is 100 feet wide. You can walk along the river at a speed of 5 ft/sec or swim across the river at a speed of 3 ft/sec. What path should you take? A: Which of the following quantities are y.. 2022. 12. 6. [Notes & HW Answers] 4.2 Optimization [Prepwork 4.2] Q1. Which of the following examples satisfy the hypotheses of the Extreme Value Theorem on the given interval? (A) k(x)={3x^2+9 for 0≤xf(x)=2x^3−12x^2+18x+16. Find the minimal value of f(x) on the interval −1≤x≤2. Answer: The minimum value of f(x) on this interval is −16 and occurs at x=−1. Q3. Suppose f(x)f(x) is a continuous function defined on −∞𝑔(𝑡)=6𝑡𝑒^(−5𝑡) if 𝑡>0. A: global.. 2022. 12. 6. [Notes & HW Answers] 4.1 Using First and Second Derivatives [Prepwork 4.1] Q1. Suppose f(x)f(x) is a continuous function that has a local maximum at the point (3,2).Which of the following statements must be true? A: (1) If a is just a little greater than 3, then f(a) ≤ 2. (2) f(x) has a critical point at x=3. (3) If a is just a little less than 3, then f(a) ≤ 2. Q2. Suppose f(x)f(x) is a continuous function that has a local minimum at (1,6)(1,6) and no o.. 2022. 12. 6. [Notes] Ch.21 Applying Computing to Engineering Problems (Runestone) I. Warm-up: Binary Search 1. Binary search repeatedly divides the search space (the values you are searching through) in half. 2. In the best case scenario, the first value that you look at is the optimal braking coefficient. II. Introduction: Algorithms and Data Structures 1. Algorithms & Data Structures (1) Algorithm: a set of steps to solve a computational problem We need to choose the correc.. 2022. 12. 6. [Notes] Ch.20 More Data Structures (Runestone) EXERCISE) Printing a Vector of int Write a function that prints out the contents of a vector of int. II. Vectors of Vectors 1. Review: declaring the element type of a vector (1) Declare a vector like this: => In addition to the base type of vector, provide the type of elements it will hold. (2) A vector can store elements of any type, as long as they match the type with which it is declared. 2. .. 2022. 12. 6. [Notes] Ch.19 Structs (Runestone) I. Introduction 1. Modeling Real-World Objects in Code (1) Let’s model the autonomous rovers used to explore the dark side of Proxima b. => This proliferation of variables will quickly become unmanageable. (2) Using vectors: Vectors can store sequences of objects => We no longer need an arbitrary large number of variables. The vectors just grow to accommodate new rovers. => However, each attribu.. 2022. 12. 6. [Notes] Ch.18 Program Design in C++ (Runestone) I. Introduction 1. Bottom-up design: starts by identifying specific features that we’ll need in our program, and then writing functions that accomplish these specific features. 2. Top-down design: starts by looking at the big picture of what the end result will be, and then breaks it down into smaller steps after that. II. Bottom-up Design We need to first think of some small pieces of functiona.. 2022. 12. 5. Umich ENGR 101 Project 4 Overview (Summary) [I. Project Roadmap] 1. Helper functions 2. Checkpoints (1) Read in data files: planet info (2) Create a vector of vectors to represent the map (3) Place the planet symbols in the correct location 3. Driver program (1) Match planet names with their locations (2) Fix the corrupted data (3) Implement the Nearest Neighbor algorithm to plan the route for the gLyft driver (4) Verify : journey.txt fil.. 2022. 12. 1. [Notes] 3.10 Theorems About Differentiable Functions 2022. 11. 29. [Notes & HW Answers] 3.9 Linear Approximation [Prepwork 3.9] Q1. What is the value at x=.1 of the local linearization L(x) of (1+x)^5 at x=0? A: L(0.1) = 1.5 Q2. Suppose you use the tangent line approximation near t=4 to estimate s′(4.05), where s(t) is a function that is always concave up. Then your answer is an A: underestimate Q3. Suppose the linear approximation of g(x)g(x) near x=6 is given by L(x)=5(x−6)−12. A:Then g(6) = -12 and g'(6.. 2022. 11. 21. 이전 1 2 3 4 5 6 7 8 9 다음
