Q4. Solve the following by using Laplace Transform (i) sin 2te-t + 3 t5 - cosh t 2 t (ii) sin + cost+t sin t 2

Q: Given the Taylor polynomial for f(x) at x = 3, find ƒ(³) (3) T₁(x) = 1 + x −3+2(x − 3)² + 2(x-3)³ -…

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Q: 1 Solve by using power series: 2 y'-y = cosh(x). Find the recurrence relation and compute the first…

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Q: The throttle-control lever OA rotates in the range 0 ≤ 0 ≤ 90°. An internal torsional return spring…

A: Please see the attachment

Q: / Reversing the order of integration fxsinydydx.

A: To find- Reversing the order of integration ∫0π∫0xxsiny dy dx

Q: Find the general solution of the DE

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Q: In Boolean ring R, if a is an element in R then a is O (i) idempotent O (ii) nilpotent O (iii) zero…

A: Boolean ring is a ring in which every element is of the form x2 = x .

Q: Consider the minimization problem min a² + x²+2x3 s.t. 110 011 [B] - [3]. Given the initial guess…

A: As per the question we are given a minimization problem and we have to find the optimal solution…

Q: 3. Express the equation y = mx + b, where m and b are constants, in plane polar coordinate.

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: ind Laplace Transform of the expression. f(t) = e-5 H (t-2)

A: Sol Le-tHt-2 Apply transform rule:  if Lft=Fs then  Leatft=Fs-a

Q: Exercise 2 Using the Laplace transform and showing the details, sovle the IVP y" + 3y + 2y = { 1¹ 0…

A: Here we use the properties of Laplace transform from table of Laplace transform to answer the…

Q: …) Find the half-range sine series for the function f(t) = πt - t², in the interval 0<t<π.

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Q: (7) The set H={0,1,2}is a subring of (Z4, +4,.4) integer ring module 4. T OF

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Q: d) Give a formula for the coefficient of ak in the expansion of where k E Z. 100

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Q: 4 The result of ff*(+√y) dxdy=

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Q: Q1\ Answer only two of the following questions: A\ Evaluate f sinx esecx cos²x dx. [15] [8 4 3 1 B\…

A: We have to solve the given problems.

Q: + ax ax²y + bxy² + 2y³ be (x, y) its harmonic conj en la + b + v(1, 1) is ec

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Q: 4. Find ez dz fa-1+31-8 (3² + 1)(= + 9) |z-1+j|=/

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Q: Let 101 A = 12 12 15 1 1 0 1 1 (a) Find a basis for the column space of A. (b) Find a basis for the…

A: Let A=101112121511011   (a) To Find: A basis for the column space of A.   (b) To Find: A basis for…

Q: The graph G₁ has 6 vertices, all of degree 3. How many edges does G₁ have? The graph G₂ has 8…

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Q: The conjugate harmonic function v(x, y) of u = In (x² + y²) is

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Q: 2. Determine the area of the region that is simultaneously interior to the curve r = 2 + cos (30), e…

A: Given that, An area is simultaneously interior to the curve r=2+cos3θ, and exterior to the curve…

Q: 4/(A)Find the derivative of f(x, y) = xe + cosxy at the point (2,0) in the direction. дz (B)If Z =…

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Q: Consider the vectors x(¹) (t) = ( ) and x(²) (t) = ( 6 ). 6t (a) Compute the Wronskian of x(¹) and…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Example:- Evaluate the integral of the region R* enclosed by applying the transformation u = ²x-³, v…

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Q: Q1: Find the general solution for the following first order D.Es? (Answer two only) a) sinx+cosh…

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Q: Construct a finite state automaton that recognizes all strings that end with 11.

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Q: 2 Express (+) in polar form O 3 [cos 67+isin 67] O 13 [cos 70+isin 70] O 3 [cos 70+isin 70] O 13…

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Q: show that the following function @f(z)=3z²+57-6 are analytic

A: Sol

Q: Let g C[0, 1] be a fixed function. Consider the operator A = B(C[0, 1]) defined by (Au) (s) :=…

A: Compact Operator: A compact operator is a linear operator A:X→Y where X, Y are normed vector spaces…

Q: (²+1) ecosx cotx y² dy cosx dx

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Q: Find the directions in which the function f(x,y) = x²y + e* sin(y) Increase and decrease most…

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Q: 4. Find the magnetic field at: a. Center solenoid with long 20 cm, 1.4 cm radius and 600 turns…

A: Here, we use the magnetic field formula due to solenoid to get the solution.

Q: 5/ change the cartesian integral in an equvalant polor integral then evalute 2x-x² the polor…

A: First we change x and y into r, theta form means polar coordinates  x=rcos(theta) y=rsin(theta) Then…

Q: The complete solution of the ordinary differential equation d² y dx² + P dy dx + qy = 0 is - 3x…

A: We have to find the values of p and q  To find p and q we use general solution the process given…

Q: How to find the inverse Laplace transform of the expression? (3s-5) / (4s2+4s+1)

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Q: Multiply the following fractions using the array model method described in the video lesson. Make…

A: To multiply a/b with c/d using array model method, draw b columns and fill a of them : draw d rows…

Q: Find the standard matrix of the linear transformation T: R² → R³ given by T(x₁, x2) = (2x₁ - 3x2, x₁…

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Q: 7. Find the eigenvalues and eigenvectors the system X'= [30. Use the eigenvalues and eigenvectors to…

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Q: Jse partial fractions to find the inverse Laplace transformation of the below Determine L−1 { 4s - 5…

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Q: Given the partitioned matrix A = [ B]. B]₁ C D in which B and C are invertible. Which of the…

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Q: Calculate the curl of the vector = (2x + 3y)i + (y+z)j + (xy + 2zx)k

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Q: 30Find the Laurent Series of 3 flz 1: J = C:/Z/=1 (2-1)2 (2-3)

A: We find Laurent series of given function.

Q: Q1/ Find maximum,minimum OULE ,and saddle point of the surface Z = x³y³ - 12x + 3y + 12.

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Q: Give the domain of f, the domain of g, and the domain of m, where m(x) = f[g(x)]. f(u) = In u;…

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Q: Compute a 4-decimal place value of Log(11.7) from Log(11)=1.041, Log(12)=1.079 using linear Lagrange…

A: Please see the attachment  Log (11.7) = 1.0682 (actual value)  And approximate value = 1.0676  %…

Q: Given that f(x)={kx2+2,≤22kx,x>2. If limx→2f(x) exist, then k equals.

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Q: Find with sketch the Fourier coefficients and Fourier series of the function fx) defined by f(x)= x²…

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Q: The transformation T : R² → R² given by T([21]) = [27/1 True False [2x15x₂ + 3] x1 - x₂ - 1 is a…

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Q: Let K be integer ring module 12 and let I=([4]) and J-([6]) be ideals of K. Then ([0])

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Q: Find the absolute maximum and minimum values of D(x,y)=x²-xy + y² + 1 On the closed triangular plate…

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