let (x,y,z) be Scalar Field and F a vector field.. $ Derive expression for D. (OF) and * (OF) in terms of operations applied to $(x, y, z) and F

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A: Alea wants to buy a $150,000 home. She plans to pay 16% as a down payment and will take out a 35…

Q: 6 The vectors v₁ = -6 and V₂ = 4 orthonormal basis for W. 9 2 13 2 3 form an orthogonal basis for W.…

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Q: 3. Find the optimal strategies and the value of the game for the following payoff matrix: PLAYER 2…

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Q: (e) $₁ = 5 and Sn+1 = √√4s +1 for n ≥ 1.

A: Given s1 = 5 and sn+1 = 4sn+1 for n≥1

Q: 2.f(t) = cosh wt sin wt

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Q: 2.) 1 - 4! 7! - 03 10! +

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Q: Let G(x) = [² w(t) dt. -2 Find a function, w, and a number, a, such that G(x) = 4x−² – 1. w(x) = a "

A: Evaluation of the integral

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A: Determinant of the matrix  Determinant of the matrix exist only if the matrix is square matric  It…

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Q: What is the simplified logical expression of (p A q) → (p→q)? Answer:

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Q: Describe the graph of the equation: r = 7ti - 8j + (1 + 9t)k. [Choose the correct answer.] O The…

A: .

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Q: 3. Use the surface integral is Stokes' Theorem to calculate the flux of the curl of the field F…

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Q: EVALUATE § 7. d² USING STOKE'S THEOREM 3xz^ + ex² ₁ + 2xy^ с F(x, y, z) = 3XZ1 te C IS THE CIRCLE…

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Q: Series solution of variable-coefficient ODE Consider the variable coefficient linear second order…

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Q: 4:²+4 if zi Let f(2)= 8i if z = i (a) Calculate limf(z) using properties of limits. (b) Use the e-6…

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Q: 2. Show that the following initial value problems are well-posed. (a) y=1-y, 0≤t≤ 2 y(0) = 0. (b) y…

A: We can solve this using Euler method

Q: Series solution of variable-coefficient ODE Consider the variable coefficient linear second order…

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Q: 5. The Bernoulli's form of the differential equation xdy-[y + xy ³ (1 + ln x)]dx = 0 is In

A: Bernoulli's differential equation.

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Q: 1. Find the antiderivatives of the following functions using the substitution rule. Write your…

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Q: 13. Let g: R2 → R be a function given by xy x+y g(x, y) = { 0; if (x, y) = (0,0) (a) Show that g(x,…

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Q: Solve the problem. Given the total-revenue function R(x) = 7600x, and the total-cost function C(x) =…

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Q: Compute the flux of the vector field F(x, y, z) = 3xj + 3yk through the surface S, where S is the…

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Q: Define T: (C¹ [0, 1], || · ||…) → (℃ [0, 1], || ||) by Tf = f'. Show that T is not continuous. Is…

A: T:C'[0,1], .∞→C'[0,1], .∞ T(f)=f' Let f(x)=xn then T(x)=nxn-1 T(x)=nxn-1 as n→∞,   T(x)→∞ So T is…

Q: 10. Σ 1|n+1 n=1 (n²+1)² (n²+3)

A: Given that ∑n=1∞-1n+1n2+12n2+3   we have to find out its sum

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A: We answer only one question at a time , so we will answer the first question since the exact one…

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Q: Solve the differential equation: * (D² - D-2)y= = COS X Your answer

A: The given differential equation, D2-D-2y=cos x....(1) is a non-homogeneous differential equation…

Q: Higher Order Differential Equations Solve the differential equations: a) (D^4 - 1)y = 0 b) (D^2 - D…

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Q: QUESTION 2 Suppose a relative of yours asks to borrow $50, which they agree to repay with $15 simple…

A: we have P0=$50I=$15 we will use the formula A=P01+rt

Q: 2. Use a parametrization to express the area of the given surface as a double integral and then…

A: Given ,x2+y2+z2 = 22       _________(I)and z = x2+y2     __________(II)Putting the value of z from…

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A: Let us consider the given function z=f(x,y) Determine D(x,y)=fxxfyy-(fxy)2 The maxima/minima is…

Q: A periodic function f(x)=f(x+27) is given by -7≤X<0 2 f(x)= A-X , 0≤x≤a 2 (a) Sketch f(x) and state…

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Q: 7. How many non-negative integer solutions are there to the equation X1 + X2 + X3 + 4 = 16 such that…

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Q: Evaluate (2x - y) dx + (x + 5y) dy. C: x-axis from (0, 0) to (0, -5) and (0, -5) to (7,-5)

A: The given integral is ∫C2x-y dx+x+5y dy where C is the line from 0,0 to  0,-5 and  0,-5 to 7,-5. To…

Q: f(x) = e²x cos(x)

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Q: +00 -- ) [n − 1, +c) = (0.

A: Solution :-

Q: Consider the statements about the surface of equation: n²y z = y² sin x + and the point P (1, 2) in…

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Q: Let H = {β ∈ S5 : β(4) = 4}. Prove that H is a subgroup of S5. (Reminder: The group operation of S5…

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Q: 5. Find the work done by F = (x² + y)i + (y² + x)j + ze²k over the following paths from (1, 0, 0) to…

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Q: An urn contains 2 red, 3 yellow, and 2 green balls. A ball is drawn, record its color, and without…

A: A probability tree diagram is used to represent the probability of occurrence of events without…

Q: Let p and q be points in R³, then p-q ≤||p||||||- = Hint: (a1, a2, a3) - (b₁,b2, b3) = a₁b₁ + a2b₂+…

A: Let p=p1,p2,p3 and q=q1,q2,q3 Angle between p and q is θ Dot product of p and q…

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A: First obtain the five number summary then use the formula for interquartile range (IQR), i.e.,…

Q: (a) Find x, y el such that x+y || x || .. = 1 = || y || = || ** ||**y. ∞o 2

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Q: B. A firm manufactures 2 product, A and B. Each product is processed by machines, M₁ and M₂. Each…

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Q: (b) Evaluate the following integrals: z²+cosz (i) [ezsiniz) + + sin22]dz, C: |z| = counterclockwise.…

A: (i) Given integral is∮Cezsinz+z2+coszz10+sin2zz2dzC: z=π2 counterclockwise.The integral is evaluated…