• Q2/ Using Lagrange multiplier method to find the maximum and minimum value of the function f(x, y) = x² + y² − 2x - 2y, subject to the constraint x² + y² = 4.

Q: 2 x² = 3y² +4z²

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: 4-G Given that A= (1) AB (ii) B (iii) AT 1-2 1 3 5 0 2 06 and B-3 1 2, determine 4-13,

A: Since you have posted multipart question and we can answer three subparts. So, answered the first…

Q: f(s) = s² +5 2 3s³+2s²+5s find f(t)

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Q: If Q, R, S are sets then QU(ROS) and (S-(QUR)) U (R- (QUS))) are disjoint sets.

A: This is a problem of the set theory.

Q: ƒ(a + x) = f(a) + Σo_ x² d(n)f(x) an)f(x) = f(a) + xƒ'(a) + —ƒ"(a) + ¹ƒ''(a) + ·· . =1 n! dxn x=a By…

A: The Taylor series about a point a is already given . We will use this for f(x) = sin x and a=45°

Q: (a) 2 2 (b) 1 3 11 BE 5 (c) 2 3 LEE 1 4 ○..

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Q: Which of the following functions are of exponential order? (a) t³ sint (b) 100e49 (c) e¹³

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Q: find solution using direct integral method for the partial differential equation below: გ37 əx² əy =…

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Q: 40y = 0, where y(0) = 0, y'(0) = -2

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Q: 4.1. Derive the heat equation with a metal rod with variable cross-sectional area A(x). Using the…

A: here, We have to derive the heat equation with a metal rod with variable cross-sectional area A(x).…

Q: = 72. P(₁,1) and P(r2, 82) represent the same point in polar coordinates, then ri

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Q: Solve the initial value problem. Express y explicitly in terms of t. dy t = dt y (1 + f²) y(1) = -2

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Q: Find the general solution to the differential equation (7x+5y)dx + (5x - 8y³)dy = 0

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Q: Sketch the domain of integration of the double integral (√(1-x²) La d.x dy x+y √(x² + y²) 0 0 and…

A: We will find boundary curve for domain of integration  . To find value of integral we will use polar…

Q: Identify the counterexamples to this universally quantified statement Vxx²x), where the domain for…

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Q: Complete the table shown in Figure 2 for the N = 5 data points, and hence solve the following system…

A: Solution

Q: [4] Let f(x) = = {₁2 of f. (b) (c) (d) Sketch the odd periodic extension of f. 1 (e) Find the…

A: The given problem is to find the Fourier sine series of given periodic function with given period.

Q: Assuming that all matrices are n x n and invertible, solve for D. BCAT DCBTA = BCT. OD = C-¹A BA-¹…

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Q: 10. Is there any value of k that will make the planes kx + 2y-2kz + 3 = 0 and x-2ky + 5z = 0…

A: Given planes are kx +2y -2kz +3 =0x -2ky +5z =0   Rewrite the equation: kx +2y -2kz  =-3  x -2ky +5z…

Q: How many derangements has the set. S? How many derangements of S have 9 in the 2nd position and 1 in…

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Q: Let X = (6, 7, 8, 9) and let the relation R on X be given by R = {(x, y): 3 zc N₁ x + z = y), where…

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Q: The curve defined by any parametric equations X = f(t), y = g(t) is always a function.

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Q: Find the y(t)

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Q: 3. (a) How many positive integers divide 10!. (b) How many partitions does the set [10] = {1, 2,…

A: Given, set={1,2,3,4,5,6,7,8,9,10} we have to calculate number of partitions required in which each…

Q: 10. Is there any value of k that will make the planes kx + 2y-2kz + 3 = 0 and x- 2ky + 5z = 0…

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Q: Which of the following represents the area of the region bounded by y = 2, x = 0, y = 0, z = 0 and y…

A: Use the given information.

Q: 5. In how many ways can 7 boys be seated in a circular order?

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Q: 5) By using Stokes' Theorem, find the work performed by the vector field Ex² + 4xy³i+ y²xk,on a…

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Q: f(x) = x³, y = 1, x = 1 Find the volume of the solid obtained by rotating the region A about the…

A: Solution :

Q: I. In each item below, show whether the following is TRUE or FALSE. Support your answer with a…

A: a. True, because 36=12×3 b.

Q: 2. Let S be the set [9] = {1.2..9}. 1 (D) How many derangements of S have 9 in the 2nd position and…

A: We have the set 9=1,2,...,9 We need to find the number of derangements. There are 9 places to fill…

Q: 12. What is the equivalent equation in spherical coordinates of the equation x² + y² = 6y? (a) p cos…

A: Rectangular coordinates to Spherical coordinates:                       x=ρ sin ϕ cos θy=ρ sin ϕ sin…

Q: 2Fn>Fn+1 for n>3 true or false?

A: Given,       2Fn>Fn+1 for n>3

Q: 5. The dimensions of a cylindrical object are increased by a scale factor of 3. The volume of the…

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Q: Prove (((LOM)-N) U(N-(LUM))) < (LU (MUN)) L, M, N are sets.

A: Follow the steps.

Q: (a) the volume of R using cylindrical coordinates with dV = r dz dr de where R: 0< x≤ 1,0 ≤ y ≤ √1-…

A: see my solutions

Q: If v (x, y, z) = 6i-12j+7k find 1) Divergence of v. 2) curl of v.

A: Solution :

Q: b) Solve the differential equation y(1-ysin(x))dx + (2x+3ycos(x))dy=0.

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Q: Suppose y=5 cm, Y=0.1 radians, and X=1.4 radians. Determine the following quantities. Tip: Draw your…

A: The problem is solved using the sine rule.

Q: Q1: If the function f(x) define as f:R → R such that f(x) = x+1, x>2 x²-1, x≤2 Show that the…

A: O

Q: Compute T₂(x) at x = 0.8 for y = e* and use a calculator to compute the error |eº – T₂(x)| at x =…

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Q: dx 3. Evaluate the integral I = S₁ x² + 6x +10 Include 4 decimal places on your computation. a.…

A: Given  I=∫01 dxx2+6x+10 Here a=0, b=0 anf f(x)=1x2+6x+10

Q: 4. Assume that T: R² R³ is a linear transformation. Find the standard matrix of T if 1 0 T(e₁) = [].…

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Q: (III) Find the Half-range Sine series of f(x) = sin(x) on (0,2).

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Q: Brandon is on one side of a river that is 70 m wide and wants to reach a point 250 m downstream on…

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Q: hi: Z12 → 26, i = 1,2 is the homomorphism of the circuits a 2xmod (6) = a) h1 (x) b) h2 (x) = xmod…

A: This is a question of abstract algebra.

Q: ΣΣ8.5 = t=1j=4

A: As per our guidelines we are supposed to answer only one question. Here first question answered.

Q: 5. Let A be the linear transformation R2 R2 that first reflects vectors across the line y=z, then…

A: see my solution

Q: Find the present value of payments of $300 made at the end of each six months for eight years. The…

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Q: (a) Compute the Jacobi symbol (237), showing all working.

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