1. (Due September 1) We say that a function f(x) is scale-shift-invariant if for every λ>0, there exists a value yo for which y = f(x) implies that y' = f(x'), where y' = y + yo and x = 2 * x. Write down, in detail, the proof that if a differentiable function is scale-shift-invariant, then f(x) = A + a* ln(x) for some A and a.

Q: Use induction on n to show that η k=1 k4 = 15 5 η + 1 η* + 2 1 3 3 1 ·η. 30

A: To prove any relation using mathematical induction we need to use 3 steps  step1 : Prove the…

Q: 4. Test the existence and uniqueness of solutions of the initial value problem: dy 2xy y(-1) = 1 dx…

A: The given differential equation is dydx=2xy4+x2+y2.      y(-1)=1. To Check: Existence and uniqueness…

Q: es lls ew zeiflucifiib ons einiseen stigesber Show that for neN, (2n)! ' (r!)² ((n −r)!)² - 7=0 2n -…

A: We will use binomial expansion to prove given relation

Q: the best method to find the polynominal for a given data of unequal interval is

A: To find: The method to find the polynomial which is best to use when data is of unequal interval.…

Q: The Z-transform of the following function f[k] = 2 + (-5)* - 33 (-4)* is 42 so the constants A and B…

A: Here the given function is f[k]=942.2k+517.-5k336-4k We will find Z-transform of the this function…

Q: Find the roots of an equation f(x)= x^3-x-1 using four iterations of bisection method. Compute also…

A: Sol:-  f(x)=x3-x-1Here x 0 1 2 f(x) -1 -1 5 1st iteration :f(1)=-1<0 & f(2)=5>0∴…

Q: at 0 to approxmate We will use the degree 4 Taylor polynomial for e -22 10.27 -² dz First enter in…

A: We can use the Taylor series of ex to find the polynomial as per the question.

Q: 5. For the given system, use Gaussian elimination to obtain an equivalent system whose coefficient…

A: Consider the given system of equation, x1-2x2=32x1-x2=9 So, the system of equation is written as,…

Q: Find the imvesse Fourrez transformation of F (P) = eply; y = (-00,00). Є

A:

Q: (ii) Find Gx(t) = E (tx) when X is a geometric random variable; i.e. for a {1,2,...} it is that P(X…

A:

Q: G] Example: Raggs, Ltd., a clothing firm, has fixed costs of $10,000 a year. These costs, such as…

A:

Q: Use the final value theorem, the final value of f(t)=6. (et +2) - 10 is.....

A:

Q: Show that convolution with a given function f commutes with differentiation; that is, show that…

A:

Q: onuts is $0.60, and profit per cake is $3.25. It takes 1/6 labour-hour to make a dozen donuts (using…

A: Let x represent the dozen of donuts and y represent the dozen of cakes . according to given…

Q: Exercise 1) 2) 3) 4) 5) 6) 7) 2xyỳ = (y)² + 1 2xỳ = (y)² – 1 - (y-x)ỳ - y = 0 ỳ + (y)³ = 0 ỳ te-ỳ=0…

A: Disclaimer:  Since you have posted a question with multiple sub-parts, we will solve first three…

Q: Consider the following vectors: a = 1 V3 = For each of the following vectors, determine whether it…

A:

Q: 5. x = A sin (at + B); w a parameter, not to be eliminated.

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 2. Find the maximum and minimum values of the function f(x, y) = x² + y² − x − y + 1 on the…

A: Given: Let us consider the given function fx,y=x2+y2-x-y+1 and the vertices 0,0,2,0, and 0,2. To…

Q: Exercise 2.16. Prove the formulas for the equations of lines in the Hyperbolic Half-Plane model.

A: Solution:- In a hyperbolic half-plane model , we use the following definitions ; h-point: any point…

Q: The blue curve on the following graph shows the height of an airplane over 10 minutes of flight. The…

A: Consider the point A and take two points on a line passing through A and tangent to the curve. It…

Q: The marginal gain from Sam's third hour of work, from 10:00 AM to 11:00 AM, is 40 problems. Later,…

A:

Q: Use the 4th order Runge-Kutta Method to Solve the differential equation dy ax==(x-x-1)=²72 to find…

A: Given: dydx=y-x-12+2, y(0) = 1, h = 0.2We have to find y(1) and percentage error. Also, the exact…

Q: -1 3. Show that sin-¹x = tan X √1-x² if |x| < 1.

A: Introduction: When there are trigonometric functions present in an expression or equation,…

Q: The characteristic equation of the matrix is 2³-122 - 16 = 0. The reduction of the matrix expression…

A:

Q: Prove the identity; verl 2n 2n 2n (264+1)=(2²+1) + 2(2²)+(2²1) n sen of eliges lls ew zeitluciflib…

A:

Q: Find_ƒ¹(0.8) & ƒ¹¹ (0.8) using quadratic interpolation.

A:

Q: Question: Inside in the House Look for four (4). objects(except: Flower Petals, Sunflower, Banana,…

A: We need to explain one example of Fibonacci numbers that can be observe in home.

Q: Prove and illustrate by an example. V(fg) =fVg+gVf

A:

Q: DE 2 1. xy(5)-(4) + x²y"" = 2yy' TYPE ORDER DEGREE LINEARITY

A:

Q: Determine whether the graph shown hasdirected or undirected edges, whether it has multiple edges,and…

A: We have the graph: The graph has undirected edges, as the direction of the edges is not given.

Q: 1. Triangle inequality for inner products: For all a, b, c € V, (a, c) ≤ (a, b) + (b, c). = 0 and…

A:

Q: a.Determine whether the graph below is bipartite b. Draw the graph of K4,4

A: Given: a) A graph  To determine: a) Whether the graph is bipartite. b) Draw the graph of K4, 4.

Q: 19-22 Show that the equation represents a sphere, and find its center and radius. 20. x² + y² + z² =…

A:

Q: Quick question is that 2500 and 5000feet per minute ?

A:

Q: Obtain a numerical solution of 2y + y - x=0 using Euler's method with step size equal to (0.5) and…

A:

Q: Exhibit an explicit bijection between parking functions on [n] and rooted forests with n vertices.…

A: Given below clear explanation

Q: -0-0 and 2- For the two vectors: U- cijkuivjek find the result of the expression:

A:

Q: If x² [x = a (1) r*²+a(²), x-(2-3)+(2) = t² is the complementary solution of the nonhomogeneous…

A: To find- If xc = c112t-1 + c221t2 is the complementary solution of the nonhomogeneous system x' =…

Q: tain z = 올n (+롤)

A: Solution :-

Q: Given the graph of f(x) = √√x as shown, graph the function - 5ƒ(x) – 1.

A:

Q: The system of equations: -10x1 + 2x2 + x3 + x4 = -3 2x1 - 10x2 + x3 + x4 = -15 x1 + x2 10x3 + 2x4 =…

A: Given :  -10x1+2x2+x3+x4=-32x1-10x2+x3+x4=-15x1+x2-10x3+2x4=-27x1+x2+2x3-10x4=9 To Find : x1 , x2 by…

Q: The Z-transform of the following function f[k] = 2.2k +$.(-5)* - 3 (-4)* 33 is 42 so the constants A…

A:

Q: Consider the following system, y" = f(x), y(0) + y'(0) = 0; y(1) = 0, and a. Find it's Green's…

A: Given : y"=fx   ,  y0+y'0=0  ; y1=0 To Find : a . Green's function             : b . Solution for…

Q: The Z-transform of the following function f[k] = 2 + .(-5)*-(-4)* so the constants A and B…

A:

Q: 1 + 1 + 1 + 1 + 1 1 + 1 + 1 + 1 + 1 1 + 1 x 0 + 1 = ?

A: Given, 1+1+1+1+1+1+1+1+1+1+1+1*0+1 =. ?

Q: For Exercise, use mathematical induction to prove the given statement for all positive integers n. 3…

A:

Q: Find the approximate error, relative approximate error, and absolute relative approximate error of…

A: The approximate error is calculated using the formula: Ea=Present value-Previous value. The relative…

Q: 1. Let - be a relation over Zx (Z\ {0}) defined by (a,b)-(c,d) iff ad = bc. Prove that this is an…

A:

Q: Find the equation satisfied by the squares of the singular values of the matrix associated with the…

A: Given the equations 2x+3y+z=0x-y-z=12x+y=02y+z=-2

Q: Equivalent Descriptions of Interior of an Angle. In possible definitions of the interior of an…

A: Here, in the question, its given about the description of interior of an angle. One of the defintion…