The function f(x) = |ax - b| + c|x| : x in (-∞, ∞), where a > 0. b > 0 , c > 0 Find the condition if f(x) attains minimum value only at one point.

Q: Problem 6. Let V and W be finite dimensional vector spaces over IF. (a) Show that there exists an…

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Q: Consider the following linear system of differential equations: x² = x + z y = x + y z' = -2x - z

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Q: Suppose f(x, y) = (a) ▼ f(x, y) = (b) ▼ f(-0.7, 7) = tan(x) + y and u is the unit vector in the…

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Q: F(t) = 5.2t+1-3 500t-1500 t-1 for 0 4

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Q: Determine whether T is a linear transformation. T: Mnn --->R defined by     T(A) = rank(A)

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Q: The City Housing Authority has received 75 applications from qualified applicants for ten low-income…

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Q: Find the mass, the moments, and the center of mass of the solid E with the given density function p.…

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Q: 3. f(t) = cos 4t-cos 2t t

A: We know that  LFt=fs=∫0∞e-stFtdt           aLcosat=ss2+a2                         bL1tFt=∫s∞fxdx…

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Q: characterize the following differential equation (what order is it, if it is linear or not, if it is…

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Q: -27 The inverse Laplace transform of s² + 81 is Asin(bt), where A and b are constants such that b> 0…

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Q: 4. u(0, 1) = 0, u(π, t) = 0, t>0 0<x< π/2 u(x, 0) = = π-x, π/2<x<T 13.3 Heat Equation 72

A: We solve the problem by the method of Saperation of variable. In this method we consider the…

Q: Find the zero/s of the function f(x) = In(4x) - 3 using Newton Raphson Method. (Use 6 decimal…

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Q: Иху = вги тих a, y" +ary" +asy tary = exy агу" азу э

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Q: Using the - definition of continuity, show that the func- tion f R³ R² defined as f(x, y, z) = xyî +…

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Q: Find a general solution of the system x'(t) = Ax(t) for the given matrix A. A = -23 - 10 20 8 5-6…

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Q: In problems use the building block = Σa", |x| < 1, together with the result 1 I n=0 for adding power…

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Q: (a) Show that for each complex number z ‡ 1, (b) Show that (c) Show that η n Στ k=0 Text Σcos(k0)…

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Q: Problem 4 Consider the following linear program: min 6x1 +4x2+2x3 s.t. x₁+x₂x3 ≥ −1 2x1 + 2x3 ≥ 1 Xi…

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Q: Construct a simple graph that is a forest with vertices P, Q, R, S, T, U such that the degree of R…

A: We will first give the edge set of the simple graph  thag is a forest with vertices P, Q, R, S, T ,…

Q: Consider the plate bounded by y2 = 8x and x = 2 with density 8 = 2-x. (a) Sketch a graph of the…

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Q: prove by some form of mathematical induction: for n in natural numbers, 9 | n^3 + (n+1)^3 + (n+2)^3

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Q: Food usually begins to become dangerous when it becomes cool enough to be habitable for bacteria.…

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A: A function f(x) is called an even function, if f(-x)=f(x) For example, f(x)=1 is an even function.…

Q: 3.9 Obtain lower and upper bounds for Y, (G).

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Q: real value of b such that f(x) has the smallest value at x = 1.

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Q: Find the average rate of change of the function f(x)=√x from x₁ = 36 to x2 = 49. The average rate of…

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Q: 6. Integrate /₁ I dr as a power series. Determine the radius of convergence. T8

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Q: 2.3. Let X1 and [2] (0) = -4. be solutions of the system Y2 where a(t), b(t), and c(t) are…

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Q: 5. Consider the set of vectors B= 8 # and the vector y=-9 a. Show that S is a basis of R³. b. Find…

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Q: Let W = {(a, 2b, b-a): a, b ER} be subspace of R³. o Find an orthonormal basis for W. • Find the…

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Q: a. Use a truth table to show that p→q and ~q→~p are equivalent. b. Use the result from part (a) to…

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Q: A car, 15 kilometers directly east of a bus, moves west at 80km/hr. At the same moment, the bus…

A: Given distance AC=15 km Let at time t their distance is minimum  Therefore at time t distance travel…

Q: Q Using Newton's forward difference Formula. Find the Sum Sn=1³2³4.1².*n ³ 13,234 (Step by Step…

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Q: Using exponential map, if e = [0.713, 0.926, 1.623], what is the vector "v"? O [0.713, 0.926, 1.623]…

A: Given that, e=0.7130.9261.623 The vector v is determined as shown below.

Q: Use a computer algebra system to find r = 4 cos 30 TL 6 p = k m= < # < (x, y) = (3.91, 0 TL 6

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Q: Question 24 Using De Morgan's law, which choice is logically equivalent to the following predicate…

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Q: A*(x) = n(t, Un)un, x≤ H. Since for all x H, A* (A(x)) A(A*(x)) = Σkn(A(x), Un)Un = Σ|kn|²(x, Un)Un,…

A: Kindly refer to Step 2 for the solution.

Q: (5) Let G be an arbitrary group. (a) Prove that the formula g*a = ga defines an action of G on…

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Q: 1- Simplify the following :- 3139-119 21-1

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Q: Prove the following using the Mean Value Theorem: (a) For any real numbers x and y with x > y, we…

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