For each q € Z+, let B, denote the set of points in [0, 1] whose image under f is at least 1/q: B₁ = {x = [0, 1] : f(x) ≥ 1/q}. Write down B₁ for 1 ≤ q ≤ 5. Show that |B|, the number of elements in B₁ satisfies 1 - |B₁| ≤ 2 + 79(9 − 1).

Q: (c) For the set A = {[0], [6]} ≤ Z12 determine the set U = h(A). Then for the set UC Z18 determine…

A: In group theory, sets like Z12​ and Z18​ are examples of cyclic groups under addition modulo 12 and…

Q: Consider V = {(2,y) : x, y ≤ R}. Let and ⋆ be operations on this set defined in the following way:…

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Q: Let F= R and V = R*. Let W, = {(x1,x2,X3,X4) € R* : x1 – x2 + X3 – x4 = 0 and x1 +x2 = 0}, W2 =…

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Q: Let f(z) be an entire function satisfying that f(z)| ≤|z² for all z. Show that f(z) = az² for some…

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Q: The moment coefficient with respect to the leading edge and the centre of pressure when the AOA is…

A: As per the question, we are tasked with calculating the lift coefficient of an aerofoil.  We are…

Q: Suppose that f(x) is convex and continuous on an interval I. Show that dif(x1) + ·.+ A„f(xn) + Anf…

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Q: 18. Determine whether each of these functions is a bijec- tion from R to R. a) f(x) = -3x + 4 b)…

A: As per guidelines, we will solve first three subparts of the question. a) Given function is fx=-3x+4…

Q: b) Let ø € Fnc(A, B) be the function that maps the position a e A to the numeric digit bEB that…

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Q: b) Let E = {0,±3,+6,...} be the set of integers that are divisible by 3 and let T = {0, +5, +10,...}…

A: Explanation of the answer is as follows

Q: ii) The zero-lift AOA of the aerofoil.

A: As per the question, our objective is to calculate the zero lift angle of attack (AOAzero lift) and…

Q: Given f(x) = v3x + 5, f:R → R where R is the set of real numbers. а) Find the domain and range of…

A: We will find out all the required values.

Q: Suppose UCC is a domain, f, g = O(U). If |ƒ(z)|2 + |g(z)|² = 1 for all ZEU, show that ƒ and g are…

A: The solution to the problem is in the segment below.Explanation:To show that f(z) and g(z) are…

Q: If X is uniform in the interval [-3,3] compute X(i.e. E{X}) and o² (i.e.E{(X-X)²}).

A: Given that X ~ U[-3,3] to find mean and variance

Q: Prove that there is an additive function T : R --> R that is not linear.

A: Let T: V→W  be the linear transformation and we it is linear,…

Q: For each of the following functions f(x) (x E R²), describe the sets V₁ ≥ 4 = { x | f(x) ≥ 4 } and…

A: A function is called convex if its double derivative is positive OR any line formed by joining any…

Q: Exercise 4. Let F and G be homothetic functions in two variables. Is their sum homothetic? [Hint,…

A: We will use the fact that the MRS of a homothetic function is always homogeneous of degree 0. Let…

Q: 5. Let F= [3,2,1] and r= [2,1,–3]. Compute the following: %3D a) Proj „F. b) Orth rF = F – Proj „F.…

A: We know that  ProjrF=r.F∥r∥2r Now, r.F=23+12-31=5 ∥r∥2=r,r        =2,1,-3,2,1,-3        =22+11-3-3…

Q: Let X = {1, (b) xm} and Y = {y₁, Yn} be finite sets. Determine the number of one to one functions…

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Q: For any subset A of R, define the function XA : R →R by if x E A 1, XA(") = 0, if x ¢ A. Let A and B…

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Q: Show that the set of functions 1,cosx,sinx,cos2x,sin2x,…,cosmx,sinmx,… is orthogonal on the interval…

A: We are given the following functions: 1, cosx, sinx, cos2x, sin2x,…, cosmx, sinmx, …   Our aim is to…

Q: 5. Let f be defined by the floor function f(x) = [] and let S = {-3, -2, -1, 0, 1, 2, 3}. a)…

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Q: 11. Define F: Z ×Z→Z×Z as follows: For all ordered pairs (a, b) of integers, F(a, b) = (2a + 1, 3b –…

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Q: Is the function f(x) = x + 1 from the set of integers to the set of integers onto?

A: For onto from set A to B, Every value of set B should exist atleast once in the function.

Q: Let φ1(x) = 1, φ2(x) = x/|x|, φ3(x) = x^2 − 1/3 for −1 ≤x ≤1. Show that (φ1,φ2,φ3) form an…

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Q: Ql: for the following function, determine the interval over which fis 1) increasing 2) decreasing 3)…

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Q: 4. Let f be defined for all real x, and suppose that \fx) – f(v)| < (x – y)? for all x, y e R. Prove…

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Q: Q.10. Let [a, b] be an interval of R. Let f:[a,b]→R be a function such that f is M-times…

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Q: If x > 0, prove that T - In (1+ x) > 2+2x

A: Using derivative

Q: 7. Find the minimum of, f(x1, x2) = 2x? – X1X2 + 2x³ + x³ – 2x1x3 And check the second order…

A: This is a problem of multi-variable calculus.

Q: 2. Let us define a. Verify that f(x, y) = af ду xy(x² - y²) x² + y² af y(x² - y² + 4x²y²) əx (x² +…

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Q: O Find the largest value of A such that the function f(x) = x + 1x? - 4x + 6 is decreasing for all x…

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Q: Find the two positive integers x and y such that x + y = 60 an 2 xy is maximum

A: The equation is x+y=60 where x and y are two positive integers. The main objective is to find x and…

Q: Find: ii) P (X₂ ≤ 1X₂ ≤). f(x₁,x₂) = {1x1x² 0≤x≤1, 0≤ x₂ ≤ 1 elsewhere

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Q: Let fi = 1+2x + 2x² + 3x³, f2 = 2+3x + 3x² + 4x³, f3 = 3+ 5x + 5æ² + 6x³ and 9i =1+x+x², g2 = 1+x…

A: Given polynomials are; f1=1+2x+2x2+3x3,f2=2+3x+3x2+4x3,f3=3+5x+5x2+6x3…

Q: 3. Assume f:{-3,0, 2, 11}{-11,0, 3, 5, 19} be a function given by f(-3) = 0, f(0) = -11,ƒ(2) =…

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Q: Let f = u + iv be analytic in the connected open set and assume u and v satisfy u? + 3v2 = 4. Show f…

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Q: or the given function f(x) = [3x + 5], compute f ({2}).

A: