Let g : B → C and h : B → C be functions. Suppose that go f = hof for every function f: A → B. Prove that g = h.

Q: Using Gauss Mean Value Theorem, find 1 sin (7/6 + 2e") d0. (Ans. 1/4)

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Q: 15. Given the graph of f (x). With the area of region A equal to 7/3, region B is 34/3 and region C…

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Q: Let the predictor variable x represent heights of males and let response variable y represent…

A: Given- Let the predicate variable x represent the heights of males and let response variable y…

Q: Find the average value of the function f(x.y) =x +y° over the rectangle R= {(xy)| 0sxs3,0sys3). The…

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Q: VI. Use Lagrange Multipliers to solve the following: Maximize f(r, y, z) = 4x + 2y + z subject to +…

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Q: 3. Suppose y(t) is the inverse Laplace transform of the following function: y(t) = L-1 What is lim…

A: We have to find the inverse Laplace transform of the given function.

Q: dy y cos x+sin y +y Solve the following 1. dx 0. %D sin x+x cos y+x differntail equation

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Q: Find the number m, such that the function y = ema is one solution of the ODE dy &y dy + 5- dx? = 0…

A: We will satisfy the solution with given ODE to get value of m.

Q: let R3 have the Euclidean inner product and use the Gram-Schmidt process to transform the basis…

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Q: Given the following results of the height and weight of 1,000 men students : 3= 68", X-150 lbs,…

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Q: Give the amplitude or period as requested. Amplitude of y = -5 cos A 8Tt В D) 5

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Q: 6. f(t)=-e" sin (2r + 7) -2t 7. f(1)= 3e " cosh (In 21) %3D

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Q: 6cis (π/2)/ 12cis (π/8) Divide. Leave your answer in trigonometric form.

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Q: Q6 In what follows, let i = v-1 denote the imaginary unit. (a) It z = 4 +5i and w = 2+4i, find 32 +…

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Q: az dz and dy *e6y. Solve for IV. Suppose z is a function of r and y, and tan Vy2 +x2

A: This is a problem of partial differentiation.

Q: . Find and classify all the critical points of f (x, y) = 7x – 8y + 2xy – x² + y³.

A: (2)  Given data curve is  f(x,y)=7x-8y+2xy-x2+y3.............(1) then fx=7+2y-2x    &…

Q: Use Green's Theorem to evaluate ſ F•dr. (Check the orientation of the curve before applying the…

A: To find- Use Green's Theorem to evaluate ∫CF·dr. (Check the orientation of the curve before applying…

Q: I. Show that the function f defined by (1, y) = (0,0) %3D f(r, y) (1, y) # (0,0) I+y is not…

A: Given                 f(x,y)=1 , (x,y)=(0,0)                           =x2+yx+y ,…

Q: Problem 1. Let a € R and u solve the 2nd order linear partial differential equation Uzz – 2auzy –…

A: Here, we are given the following 2nd order linear partial differential equation where α∈ℝ.…

Q: If n is an integer, n 180° represents an integer multiple of 180°, and (2n + 1)-90° represents an…

A: Given that if n is an integer, n·180o represents an integer multiple of 180o, and (2n+1)·90o…

Q: 10. Let C' (R) be the set of all continuously differentiable functions. Show that W = {f : f' - Af =…

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Q: Problem (1) A population P is modeled by the differential dP = P(1- dt ). The slope field of the…

A: We have to sketch the solution curves that satisfy the given initial conditions. Then, we can…

Q: Determine whether the series converges absolutely or conditionally, or diverges. (-1)"e-nª n = 0 Σ…

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Q: Give an example of a set S which is (i) bounded above but not bounded below, (ii) bounded below but…

A: (i). We consider the set which has bounded above but not bounded below

Q: Use Laplace transforms to solve the following initial value problem S y (t) – y(t) = 8 (t) y(0-) =…

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Q: 5. Let o1, 02, 03 be the Pauli spin matrices - (? ). 0 1 1 0 -(? ) 이-(69) 1 01 = 02 = i 03 and oo =…

A: We have to show that the matrices 12I2, 12σ1, 12σ2, 12σ3 are linearly independent. Then, we can…

Q: A straight flush is a 5-card poker hand where the 5 cards are consecutive in rank (straight) and ali…

A: Total cards = 52  We need to choose 5 cards. Total possible straight flesh in single suit is  A1234…

Q: Show that the determinant gives a group homomorphism det: GL(n,R)->R*, where R*=R-{0} under…

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Q: Q 2. Let f(x) = 2x, for all x E] - T, T| (a) Calculate the Fourier coefficients a0, an and b, of f…

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Q: Find and classify the equilibrium points of the system dx xy + x – 2y = dt dy (2² – 1)(y – 3) | dt

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Q: Find both the sum and difefrence of Matrix A and В. 4 -6 A = 6. 15 B= 11 - 23 -12 3 51 35 -4 71 52…

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Q: Show that g '(x) is piecewise continuous for all x, on the interval -L x

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Q: Let y(t) represent your bank account balance, in dollars, after t years. Suppose you start with…

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: To find the domain of vector function we find points where all the components are defined.

Q: Describe the graph of the equation. r = 2 cos t i - 6 sin t j+k O An ellipse in the planex = 1,…

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Q: (5a?y? - xy? + 17y2) dæ (a³y + 2a?y + 9xy + 18y) dy = 0 Solve -

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Q: 3. (1 – 3 sinh( 2t) + sinh(4t))´ dt

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Q: 3. Evaluate the following limits, if they exist: 1 (a) lim 1 +3 2x x→-0

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Q: 3. y" – 2y' + 2y = 4cos2t + 2sin2t у (0) %3D 1, у'(0) — 1 |

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Q: f (t) = 7t3 – 0.31t2 + Iạt – cost

A: Given A system that is represented by the given equation ?(?) = 7?3 − 0.31?2 + 8? − cos ?, is able…

Q: Write the Babylonian numeral as a Hindu-Arabic numeral. Babylonian Symbols Hindu-Arabic 1 10 Symbols…

A: Solution

Q: If you know f(t) = L-'{F(s)}, how would you find L-{F(s)/s² }?

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Q: Marginal Revenue The demand function for a certain boat company's 34 ft Sundancer yacht is   p = 300…

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Q: See picture f(x) = 2L periodic extension to f for all other values of x Show that f and f' is…

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Q: A 30 vector field given by V = 4ryi +3y²j +-k, represents the flow of water in a system. Use Gauss's…

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Q: Determine whether or not the vector field is conservative. If it is conservative, find a function f…

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Q: Find the compound amount and the interest earned when the given investment has continuous…

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Q: 1.) csc23ßsin3ß dß csc2 3ßsin3ß cos3ß 2.) S sin²a(seca)-5 da

A: To evaluate the given integral.

Q: 7. xdx + ydd = (x² + y²)dx 8. (2x2 + y)dx + (x²y-x)dy = 0 %3D %3D

A: We  will solve these two by the method of inspection of integrating factor

Q: Exercise 3.5.15 For n> 2, consider Z, as a group under addition (mod n) and let T denote the…

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