12. Prove the identity: tan + tan 1 sin cos

Q: [15] (4) GIVEN: z = f(x, y) = x²y, where (x, y) is subject to the constraint: I: x² + xy + 7y² 27, x…

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Q: 3. Determine the set N {(1+t,1+ yt²) : t ≤ R} CR². YE[0,1]

A: ∩γ∈0, 11+t, 1+γt2: t∈ℝ⊆ℝ2

Q: QUESTION 2 Let S(x) be a clamped cubic spline that passes thorugh the points (0,0), (1,1), and…

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Q: Exercise 3: Bijections Let X := {(x1, x₂) = R² : x² + x² = 1}. Find a bijection between X\ {(0, 1)}…

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Q: Let (x, e) and (y, d) be metric space with e(x, y) = { 1 and let fr→y be a function. Is f…

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Q: 5. Find the general solution of the boundary value problem для dμ = du +3e-2t sin 5x дем with u(π,…

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Q: • A is in RREF ● ● -689 Let A Fill in the blanks such that A has all of the following properties.…

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Q: b) Use cofactor expansion along an appropriate row or column to compute he determinant of -20 B = 0…

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Q: + x from x=1 to x = 3. me average rate of change of the function f(x)=-2x²-

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Q: 15. Let X be a normed linear space. Show that X is finite-dimensional if and only if every closed…

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Q: Suppose F(x, y) = (2y, — sin(y)) and C' is the circle of radius 5 centered at the origin oriented…

A: The given vector field is F→x, y=2y, -sin y. The curve C is the circle of radius 5 centered at…

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A: Here, the given function is x2+y2+z2≤R2 Since y≥0,the upper portion of the half sphere can be…

Q: 18. The first term of a sequence is −5 and the common difference is -8. State the general term.

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Q: Use f(x) = 2x - 3 and g(x) = 4x2 to evaluate the expression.

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Q: A solid region in the first octant is bounded by the coordinate planes and the plane x+y+z=2. The…

A: A solid region bounded by the plane x+y+z=2 in the first quadrant. The density of the solid is δx ,…

Q: 2x a. Find the local extrema of the function fix)=sin 7x on the interval 0 sxs and say where they…

A: fx=sin7x, x∈0,2π7

Q: = (an−1+ an−2+ an-3), N = 30 20. [T] a₁ = 1, a2 = 2, a3 = 3 and for n ≥ 4, an =

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Q: {79-5Z+(fғ)uis9 (ч Z{u!S(zZ-r-za) (E скорост Вимонаж 1+ 2-(2 ( ауа jод ота на Јарло бур рин (а

A: Let f(z)=(z-a)n g(z) Where g(a)≠0 then we say a is the zero of f(z) of order n.  If f(z)=p(z)/q(z)…

Q: Recall from Section 5.1 that the differential equation for the instantaneous charge q(t) on the…

A: Laplace transform

Q: What is the equilibrium payoff of player 1? PLAYER 1 Up Down PLAYER 2 Left 62,62 86,72 Right 6,28…

A: The given table is,

Q: 1. Solve the initial value problem x'(t) = [11]x(t) + [] x(0) : -=[7]. - [8 Ste³+8e³-10e 4te³ +2e³…

A: Given that, the initial value problem is- x't = 1411xt + e3t0, x0 = -27 Firstly, solve the matrix…

Q: Let f be a continuous linear functional defined on the normed linear space X. Show that M = {xe…

A: f be any continuous function on X, where Xis a normed linear space. M=x∈X|fx=0 is a closed subspace…

Q: Find A¹ and A². A = -32 -4 3 Find A1. A¹ = (Type an integer or decimal for each matrix element.)…

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Q: Given the differential equation y"+y'-2y = 0, y(0) = −1, y'(0) = 2 Apply the Laplace Transform and…

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Q: Researchers conducted a study to learn how early childhood education relates to a child's future…

A: Early childhood education refers to the educational programs and activities that are designed for…

Q: 2. Calculate the Fourier Series S(x) of f(x) = sin(x/2), -7 < x < T. What is S(T) =?

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Q: Joe takes out a home loan for $100,000. It will be repaid with 360 monthly installments beginning at…

A: The present value of an annuity is the current value of a series of equal payments made at equal…

Q: 2. Determine whether each of the following relations is a function. If it is not a function, explain…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: A chemical manufacturer wants to lease a fleet of 24 railroad tank cars with a combined carrying…

A: A chemical manufacturer wants to lease a fleet of 24 railroad tank cars. x1+x2+x3=24 Let x1 be the…

Q: Find all local constrained extrema of f(x, y) = x² + 2y - z² + z under cionstraints 2x - y = 0, x +…

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Q: 3. Sketch the graph of the reciprocal function. Find its intercepts.

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Q: 45-50. Binomial series a. Find the first four nonzero terms of the binomial series centered at 0 for…

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Q: Graph the system of inequalities. Tell whether the system is bounded or unbounded and list each…

A: The given system of inequalities is, x≥4y≤16y≥xx≥0y≥0 Concept- A feasible region of the system of…

Q: 1. Show that if the Wronskian of Y₁ and Y₂ is nonzero then so is the Wronskian of 2Y₁ and Y₁ + Y₂. 2…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: 41-42 Evaluate the triple integral using only geometric interpretation and symmetry. 41. (4+5x2yz2)…

A: An integral ∫∫∫C4+5x2yz2dV where C is the cylindrical region x2+y2≤4 , -2≤z≤2. To Find: The value of…

Q: Laplace transform a. L- (¹) 48 b. L-¹ { 1/2-) S5 C. 1 L-1 (2435) s²+3s. :-1 (432 +1} d. L-1

A: We have used standard formulae of Laplace transform.

Q: Find a public key for RSA cryptography based on the prime numbers p = 13 and q = 7. Write down the…

A: We are to find a public key for RSA cryptography based on the prime numbers p = 13 and q = 7 Write…

Q: Find the general solution of the differential equation (D4 + 6D³ +9D²)(D + 1)(D + 2)(D² + D + 1)(D²…

A: We will find the roots of the auxiliary equation.

Q: 12. True or Give a Counterexample: If fe R[a, b] then there exists € [a, b] such that f f(x) dx =…

A: The given statement is FALSE. Consider the function f:[0,5]→ℝ defined by f(x)=x+2  if 0≤x≤20…

Q: Let V be the set of vectors shown below. v={[:] V= a. If u and v are in V, is u + v in V? Why? b.…

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Q: The symmetric difference of sets A and B, denoted by AAB, is the set (A-B)U(B—A). 2. Let S be a…

A: Given that S is a sample space, Pr is a PDF on S and A,B∈P(S). (a) It is given that A and B are…

Q: Let A, B be statements. Are (A V B) V ¬(A ^¬B) and AV B logically equivalent?

A: As you have asked more than one different questions, we shall answer first Que only as per the…

Q: 6. Consider the series [ª a and ¹b. where a > 0 and b² > 0 for n ≥ 1. If [ª converges, which of the…

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Q: can be pro 25. Under the surface z = xy and above the triangle with prumozzies follow f vertices (1,…

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Q: Month Crude Oil Gasoline Month Crude Oil Gasoline 1 74 1.413 13 79 2.068 2 74 1.714 14 82 2.469 3 76…

A: Month  Crude oil Gasoline 1 74 1.413 2 74 1.714 3 76 1.571 4 75 1.889…

Q: 3. Consider the function f: Z → Q defined by f(x) (d) (e) Is fone-to-one? Justify. (f) Is fonto?…

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Q: Use the Laplace transform to solve the following initial value problem, _y" — 4y′ − 45y = 5(t−3),…

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Q: Without performing any row operations, explain why the matrix does not have an inverse. -8 26 -28 7…

A: A=-826-2871 We have to explain why the inverse of the matrix does not exist.

Q: 5. 0 3 4 8. 1 ·[₁ 3 6. 1 1 0 0 1 -1 2 4 i 17. [4 -1 1 0 00 01 0-1 0

A: Note: A square matrix A   is called diagonalizable, if it is similar to a diagonal matrix, i.e., if…

Q: n Use induction to prove: for any integer n ≥ 1, Σ(6j – 4) = 3n² – n. j=1

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