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전체 글102

[Notes & HW Answers] 3.7 Implicit Functions [Prepwork 3.7] Q1. Which of the following points satisfies the equation 𝑥^2−𝑥𝑦^2=2? A: (1) (-2^(1/2)/2, (4.5)^(1/4)) ; (2) (-2^(1/2),0) Q2. (1) Find dy/dx when x^2 - xy^2 =2. A: (1) dy/dx = (y^2-2x)/-2xy (2) Find an equation for the tangent line to x^2 - xy^2 = 2 at the point (2,1). A: (2) y = (3/4)(x-2) + 1 Q3. Find all points satisfying the equation 𝑥2−𝑥𝑦2=2x2−xy2=2 where the tangent line is v.. 2022. 11. 21.
[Notes & HW Answers] 3.6 The Chain Rule and Inverse Functions [Prepwork 3.6] Q1. Let 𝑔(𝑥)g(x) be an invertible, differentiable function with values given in the table below. 𝑥 2 5 8 𝑔(𝑥) 8 2 0 𝑔′(𝑥) -2 -0.25 -0.1 Find a formula for the tangent line of 𝑔^(−1)(𝑥) at 𝑥=2. A: y = -4(x-2)+5 Q2. Find the derivative of 𝑓(𝑥)=arctan(5ln(𝑥)). A: f'(x) = 5/(x*(25*ln^2(x)+1) [HW 3.6] Q1. Find the derivative of the function f(t), below. f(t) = ln(t^9 +8) A: f'(t) = 9t^.. 2022. 11. 21.
[Notes & HW Answers] 3.5 The Trigonometric Functions [Prepwork 3.5] Q1. The Bay of Monterey in California is known for extreme tides. The depth of the water, y, in meters can be modeled as a function of time, t, in half-hours after midnight, by y=12+6cos(t). How quickly is the depth of the water rising or falling at 3 a.m.? (Make sure you compute this in radians and give your answers to three decimal places.) Rising at (in m/half-hours) A: 1.676 Q.. 2022. 11. 21.
[Notes & HW Answers] 3.4 The Chain Rule [Prepwork 3.4] Q1. The length,L, in micrometers (𝜇μm), of steel depends on the air temperature degrees celsius, and the temperature depends on time,t, measured in hours. If the length of a steel bridge increases by 0.25μm for every degree increase in temperature, and the temperature is increasing at 4 degrees celsius per hour, how fast is the length of the bridge increasing? A: At a rate of 1 μm.. 2022. 11. 21.
[Notes & Raw Data] Lab 8. Determining a Relative Rate Law: a 'clock' reaction Keywords:relative rate law, clock reaction, oxidation, reduction, reaction, redox reaction, concentration, k', time, rate, solutions Preview the notes: Keywords: relative rate law, clock reaction, oxidation, reduction, reaction, redox reaction, concentration, k', time, rate, solutions 2022. 11. 21.
[Notes & Raw Data] Lab 7. Galvanic Cells: Electrons Flowing Spontaneously Keywords: galvanic cells, electrons flowing, electrons, copper, zinc, circuit, reactions, the Nernst equation, redox reaction, batteries, cathode, anode, cell potential, salt bridge, solution Preview the notes: Keywords: galvanic cells, electrons flowing, electrons, copper, zinc, circuit, reactions, the Nernst equation, redox reaction, batteries, cathode, anode, cell potential, salt bridge, solu.. 2022. 11. 21.
[Notes & Raw Data] Lab 6. Oxidation & Reduction: Exchanging Electrons as Currency Keywords: redox reaction, oxidation, reduction, exchanging electrons, ion, charge, reactants, products, metals, concentration Preview the notes: Keywords: redox reaction, oxidation, reduction, exchanging electrons, ion, charge, reactants, products, metals, concentration 2022. 11. 21.
[Notes] Ch.17 Vectors in C++ (Runestone) I. Introduction Indexing in C++ also uses random access to read and write data, but the indices start a 0 (just like with strings in C++). II. Declaring and Initializing Vectors in C++ 1. Vectors in C++ (1) In C++, a vector is used to store a sequence of elements. -> The elements must be homogenous (all of the same type) (2) This is conceptually similar to a vector in MATLAB, but the details are.. 2022. 11. 18.
[Notes] Ch.16 Strings, Streams, and I/O (Runestone) I. The Standard Library and # Include 1. C++ standard library (1) To use part of the standard library, use the #include directive. Ex) if you would like to use cout and cin in the code, you’ll need to include library at the top of your .cpp file #include using namespace std; (3) The using namespace std; directive is generally used with included libraries, we can use shorthand names like cout and.. 2022. 11. 18.
[Notes] Ch.15 Functions in C++ (Runestone) I. Function Basics 1. Basic structure of a function in C++ int square(int n){ Return n * n; } The function square takes one int parameter (a variable you can use in your function code), and returns an int value. Ex) calling the function: int x = 3; int y = square(x); cout 2022. 11. 18.
[Notes] Ch.14 Iteration (Runestone) I. While Loop 1. While loop (1) While loops execute a block of code as long as some condition is true. (2) If we start x at 0, and count while x < N, we iterate N times (with x as 0,1,..., N-1) 2. Hint on Creating While Loops Some of the trickier parts of writing a correct while loop are: (1) Where does it start? ex) “what gets initialized before the loop starts? And to what value?” (2) When doe.. 2022. 11. 18.
[Notes] Ch.13 More C++ Basics and Branching (Runestone) I. Implicit Type Conversions 1. int to double 1. Widening conversion: a double can always hold any integer value. (1) A double is a wider data type than an int. (2) There is no info loss in this conversion, so this conversion and other widening conversions are generally considered safe. 2. double to int (1) The double value is truncated and only the integer part of the number is retained. (2) Fr.. 2022. 11. 18.

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