1. Find the Fourier series of the function f(x) = |x| which is defined over the range - T

Q: A linear system is inconsistent if and only if its augmented matrix has a row of the form [00... 0…

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Q: (a) Show that the solution y(t) of the initial value problem y" + 2y' - 3y = 6 sin 2t, y(0) = 0, has…

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Q: Use variation of parameters method to find the following differential equations: (i) y" + 16y = 32…

A: Solution i:  Given differential equation is y''+16y=32sec(2x)           (1) Auxiliary equation of…

Q: A. Solve the following Initial Value Problem (IVP): y + 3y + 2y = 6et at y(0)=1 and y (0)=2

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Q: Solve the given initial-value problem. 1 0 2 X' = X, X(0) 1 1 2 = (²)

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Q: i think the answer above is wrong

A: given matrix 121023-113501 claim- determine if the system AX=b has  a solution for every vector b∈ℝ3…

Q: Give the points at which the given function will not be analytic. (Enter your answers as a…

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Q: Find the solution of the differential equation Dy" +1-(y')² = 0 ▷ y(0) = y'(0) = 0 V ▷ y' (co) = 1

A: The given differential equation is                                  y'''+1-y'2=0 where y0=y'0=0 and…

Q: Q(x) = √3/2+² Ser fet de Prove that & QQ (-∞ ) = 1

A: Here we can use Gamma function formula Γn = ∫0∞ xn-1 e-x dx to evaluate the given improper integral.…

Q: a) Find the root of the equation f(x) = 2cosx-x² to 2 decimal places using the Newton-Raphson…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer only in type written…

Q: 3. a) Compute: f (Rez-3z) dz where I is a directed line segment from z = 0 to z = i. b) Let C be the…

A: To Evaluate:  (a) ∫Γ(Rez-3z)dz , where Γ: z=0 to i. (b) ∮Ce-zz2(z-5)dz, where C: |z|=4 oriented…

Q: Find a vector function that represents the curve of intersection between the paraboloid 4x² + y² and…

A: We find vector function.

Q: 6 X Find the volume of the solid generated by revolving about the x-axis the region under the curve…

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

Q: Maximize: z=5x+y subject to: x-ys3 5x + 3y ≤ 75 x20, y20

A: Given,           Maximise: z=5x+y    subject to:                      x-y≤3…

Q: Let f(z) = cosh z. (1) Find the image of S:= {z = x+iye C: x<0,0 < y < } under f.

A: First calculate image the boundary line under the map. Then choose a point other that boundary from…

Q: the Maclaurin series for the following function f(x) = sin x

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Q: Suppose the row echelon form of a system of equations is x+2y-72 = 4 y-92 = 9 Enter the components…

A: We will use here the free variable t to get the solution of the given row echelon form of a system…

Q: 2. 20x₁ + 15x₂ + 10x3 = 45 -3x₁ -2.249x₂ + 7x3 = 1.751 5x₁ + x₂-3x3 = 9

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Q: Q1. Find the inverse of the following matrix by using Gauss-Jordan eliminations 1 21 -1 2 3 12₂₁ +1…

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Q: Find the angle between the vectors. (Round your answer to the nearest degree.) a = j + k, b = i +4j…

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Q: Define fct) = {est + e + cast if t 1/2 t>"/2 solve y(3) - 2 y(2) + ý' - 2y = f(t) y (0) = 1, y'(0) =…

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Q: (a, b, c, or d): . The shaded range on the right can be described using: a. (X>=0 || X=100) Using…

A: Here we will give the solution by looking at the picture only i. e. the shaded area.

Q: Use the theorem of criterion for analyticity to show that the given function is analytic in an…

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Q: (b) Find the mass of the surface S, where S is given by r(u, v) = (2uv, u²-v², u²+v²), (u, v) E D…

A: Consider the given vector equation of the surface, ru,v=&lt;2uv,u2-v2,u2+v2&gt; where, D=u,v∈ℝ2:…

Q: Q(x) = d= S2 X Prove that & QQ (-∞) = 1

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Q: Name: Questions 3) 5) 7) 57 Describing Rotations Describe the rotations. Shape A is the original…

A: Given, Shape  A. We have to describe the rotation of shape A to get position of shape B  in same…

Q: 1/2 find at: += (24)

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Q: If p is false, q is true, and r is true, find the truth value of the statement. (~pv-q) v ~r

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Q: Identify the open intervals on which the function is increasing or decreasing. g(x) = x² - 8x - 20

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Q: Determine if the integral [Inxdx converges or diverges.

A: An integrals will be divergent if the associated limit either doesn’t exist or is plus or minus…

Q: 1+ cos 0 3. For the identity 1 + sec 0 = : cos e a) Verify the identity for 0=210° using exact…

A: The given identity is 1+secθ=1+cosθcosθ. (a) Verify for θ=210°. (b) Prove the identity.

Q: Compute Edin (1)(d).

A: As per the question we are given a Dirichlet convolution between the sumof divisors function σ(n)…

Q: Find the general solution of the linear system whose augmented matrix is 1 1 2 1 1] 4 4 9 5 5 x1 =…

A: The given augmented matrix is: 1121144955 Find the Row-echelon form of the matrix.

Q: Solve the linear programming problem. Maximize P = 20x + 75y Subject to x+8y ≤ 16 x, y 20 What is…

A: For B part we need co ordinate of points where P is maximum .

Q: Ten international students who include four males and six females are friends. Each of the four male…

A: Here we show two methods to solve this problem.

Q: 1. Find the solution of the given initial value problem. y’’+y=0,     y(π/3)=2, y’(π/3)=-4 topic:…

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Q: (b) Find the points on the line r(t) = (t, 1+2t, 1-2t) whose distance from the plane 2x - 2y+z=1 is…

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Q: x²-16 -4 x +4 - ...lim تساوي

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Q: Solve the given initial-value problem. dx y − x = 6y², x(8) = = 1 dy x(y) = Give the largest…

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Q: Consider the initial value problem given below. y=-Y. (0)6 Show that when Euler's method is used to…

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Q: Use two truth tables to show that each of the propositions are equivalent.

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Q: Solve the following Initial Value Problem (IVP): y + 3y + 2y = 6e-² at y(0)=1 and y (0)=2

A: *By Bartleby policy I have to solve only first one as these are all unrelated &amp; lengthy…

Q: B. Re-write the triple integral *** following orders. 1. fff dydxdz 2. fff dxdydz dzdxdy as an…

A: Here firstly finding the curve using the limit then we saw that the region is the part of first…

Q: 3. In August, the real estate company indicated that it wanted to increase the mileage allowance to…

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Q: Consider the solid Q bounded by the surfaces S₁: Z-1 = (y-2)², S₂ : x + y = 2, S3 : x = 0, S4 : y =…

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Q: 3. With the transformation matrix (A) given by (4.20), explicitly verify that 3 Σaijaik = δjk, i=1…

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Q: b) Used bisection method to find the root of f(x)= x³ + 3x-5, Do calculation until six iterations in…

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Q: Ten international students who include four males and six females are friends. Each of the four male…

A: If choices are independent we can fill n places with p things in p*p*.......p (n times)=pn ways.

Q: Q3/A-(12 degree) If the A-¹ = 0 -1 1 11 13 25 11 -3 11 31 11 11 11 51 , Find the value of A.

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Q: 4. Let f(z) = cosh z. (3) Show that f: S→ f(S) is ono-to-one.

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