Assignment of class 02 (Chapter 1 Sections I II) 1 Match two columns appropriately
Assignment of class-02 (Chapter 1: Sections I & II) Match two columns appropriately 𝑈 = 𝐼 𝑅 Expression 𝑅1 + 𝑅2 > 𝑅3 Equation 𝐼 𝑅 + 𝑈 𝐼 + 100 Function 𝑆(𝑡) = 𝑎𝑡 + 𝑣𝑡 + 𝑆0 Formula Using the language of mathematics, the AC current is written as: 𝐼(𝑡) = 𝐼max sin(2𝜋𝑓𝑡) Call the names and their associated contents of all mathematical symbols, including 𝐼, 𝐼max , sin, 2, 𝜋, 𝑓, 𝑡, written in above mathematical expression True or False ⃗⃗ = Vectors 𝐴⃗ and 𝐵 ⃗⃗ are orthogonal to each other a) 𝐴⃗ 𝐵 b) Because it rains heavily, John has to stay at home The weather and John’s action are “orthogonal” to each other c) The speed of free fall is linearly depends on the time d) 𝑥 + 2𝑦 − = is a linear equation Let f: A B A, B and f are defined as A = {1, 2, 3} B = {5, 6, 7, 8} f = {(1, 5), (2, 8), (3, 6)} Verify whether f is a function If so, what type of function is f ? Let f: X Y X, Y and f are defined as X = {a, b, c, d} Y = {d, e, f} f = {(a, e), (b, f), (c, e), (d, d)} Verify whether f is a function If so, what type of function is f ? The distance traveled by a car is expressed as a function of time: 𝑆(𝑡) = 5𝑡 − 10 Find the domain of the function 7 Using a computer software (Excel, Origin,… or some websites, for example: https://www.desmos.com/calculator), draw the graphs of one-variable functions on same coordinate system: 𝑓(𝑥) = 𝑥 − 3𝑥 + 𝑔(𝑥) = sin2 𝑥 ℎ(𝑥) = log 𝑥 Based on plotted graphs, determine the solutions of following equation: 𝑥 − 3𝑥 + = log 𝑥 Using some websites (example: https://www.desmos.com/calculator/ongcgqgcpr), draw the graphs of two-variable functions: 𝑓(𝑥, 𝑦) = 𝑒 1−𝑥 −𝑦 𝑔(𝑥, 𝑦) = cos(𝑥) sin(𝑦) ℎ(𝑥, 𝑦) = √4 − 𝑥 − 𝑦 Determine the parity of functions: 𝑓(𝑥) = sin 𝑥 𝑔(𝑥) = 𝑥 − 3𝑥 + ℎ(𝑥, 𝑦) = cos(𝑥) sin(𝑦) If a function is neither odd nor even, please decompose it as the sum of an even and an odd function 10 Write the composite functions ℎ(𝑥) = 𝑓(𝑔(𝑥)), 𝑘(𝑥) = 𝑔(𝑓(𝑥)) and 𝑚(𝑥) = 𝑙(𝑓(𝑥), 𝑔(𝑥)) as functions of independent variable 𝑥, knowing that: 𝑓(𝑥) = 𝑥 − √𝑥 + 𝑔(𝑥) = sin 𝑥 + 𝑎 𝑙(𝑥, 𝑦) = 𝑥𝑦 + 11 The relationships between dependent and independent variables are given by: 𝑢 = 2𝑥 − 𝑣= 𝑥 + cos 𝑥 √𝑦 For each case, write parametric equations and explain the difference between them in describing practical processes