1. Find area using the definition of area as a limit along with x as the midpoint of each subinterval to find area under the curve y = f(x) = 4(x² over the interval [0,3].

Q: Solve by the Lapace Transform: y(t) + 4 y(T) (t-T)dt = 2t ²

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Q: Q2\ Solve by picard method (up to four approximation) y' + y = e* and y(0)=0 Find y(0.1)?

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Q: Q2// choose the correct answer : 3z 1) If x(n) = (0-3)"u(n) ,then Z-transform= a)x(z)= 2-0-3 b)x(z)…

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Q: Q2\ Solve by picard method (up to four approximation) y' + y = e* and y(0)=0 Find y(0.1)?

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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: Solve the given initial value problem and determine how the interval in which the solution exists…

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Q: 12. Solve the given initial-value problem X' = (₁ − ₁ ) x + ( ₁ + 1₁), X0 = (₁) X ,X(0)

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

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Q: Q3/: Find the area r = 1- cose and over the region R that lies inside the cardioid outside the…

A: Given that the cardioid r=1−cosθ and the circle r=1. We have to find the area over the region R that…

Q: 1. Write the solution of the system of equations: P₁ = 5p₁ - 4p₂ + e²t; p2 = P₁; P₁(0)=P₂ (0) = -11

A: Given system of equations are p1'=5p1-4p2+e2t,    p2'=p1   Also given p1(0)=32,   p2(0)=-11   To…

Q: [₁ F. dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = 2yi + xzj + (x +…

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Q: lim X-0 √√√x √√√x 按

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Q: Solve the given differential equation by using an appropriate substitution. The DE is homogeneous. y…

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Q: b. Find the angles 0 (with respect to the positive x-axis) associated with the directions of maximum…

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Q: 1 2. Let R be the region bounded by the curves y = x and y = x³. Let S be the solid generated when R…

A: We have to find the volume of S by both the disk/washer and shell methods and Check that results.

Q: Build the least common multiple of A and B using the example/method in module 8 on page 59860. Then…

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Q: Let f(x) = x² and g(x) = xf(x). Find c = (0,1) as guaranteed by the Cauchy Mean Value Theorem.

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Q: Find the eigenvalues and eigenvectors the system X'= [₁¹]. Use the eigenvalues and eigenvectors to…

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Q: Find the general solution of the given differential equation. (x + 1) dy + (x + 2)y = 2xe-x dx 11

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Q: (x² + y²)dx + xydy = 0 (Homogenous)

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Q: Cable AB passes over the small ideal pulley Cwithout a change in its tension. What length of cable…

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Q: + y²73, nates. Th = x direct , 8) is

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Q: Solve the given initial value problem and determine how the interval in which the solution exists…

A: Given initial value problem is y'=9ty2, y0=y0. We have to solve the given initial value problem.…

Q: Find the residues of a function 1 f(z) 3 (z − 2)(z + 1)³

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Q: By principal of mathematical induction prove that finite product of countable sets is countable

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Q: Julia is currently age

A: Given that Julia is currently age 30. She purchases a whole life insurance policy that pays a…

Q: Q1:/Verify that the given function is harmonic and find it is harmonic conjugates so that f(z) = u +…

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Q: Classify each statement as true or false. If the statement is false, give a counterexample. Part 1…

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Q: jugate harmonic f ²) in

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Q: Prove that the two fundamental answers of the second order Sturm- Liouville differential equation by…

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Q: an= 4/(5^n)

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Q: 1. A tank initially contains 50 gallons of pure water. At t=0, a brine solution containing 2 lb/gal…

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Q: newton's method -Use the function f(x) = cos²x - sin x for this problem. a. find the approximation…

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Q: 1) Using Laplace transform methods, solve for t20 the following simultaneous differential equations…

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Q: 2) The speeds of oscillation, x, of a loaded beam is given by the equation: x³ 3.25 x² + x -0.063 =…

A: NOTE: As per the guidelines we are supposed to answer only one question because of this is not a…

Q: Q1-Choose or branch ( A-find the optimum values of X₁, X2, and X3 3X1 +2X2-X3 = 1 2X1-2X2-4X3-2…

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Q: QUESTION 1 Check all statements that are true. if p is a polynomial of degree n, and q is a…

A: According to guidelines I can attempt only first three questions.. In these three questions we have…

Q: Q3\ using Euler method, find an approximate value of y corresponding to xe [0 -0.7]. Given = x(x +…

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Q: the an ¹x y is differential ec

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Q: Q1:/Verify that the given function is harmonic and find it is harmonic conjugates so that f(z) = u +…

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Q: g sequence X(n)= n. () ation property of the Z-Tra

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Q: Please find the Z transform of the following two sequences and determine the region of convergence…

A: As per the question we are given two sequences : 2-n+1 u[n-1] [(1/2)n + (1/4)n] u[n] And we have…

Q: The complete solution of the ordinary differential equation d²y dx² + P dy dx + qy = 0 is +c₂e-³x y…

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Q: Find all integer values of x for which 3x = 4 (mod 8).

A: given congruence equation 3x≡4(mod 8)

Q: solve the system. Y₁ The initial value problem Y₂ Y₂ Y""(t) + 3Y"(t) + 3Y!(t) + Y(t) = -4 sin(t),…

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Q: 3 The equation X³-X-e¹-2 = 0 has a root between x = 2 and x = 3. du a). Write five different…

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Q: (Dirichlet's function) we define f(x) こ d, if x is aration number $ otherwise, xe loi

A: Given Dirichlet's function is f(x)=1,      if x is a rational number0,       otherwise x∈0,1 We have…

Q: Fill in the blank. The symbols C₁, C₂, and k represent constants. d² (C₁ sin kx + C₂ cos kx) dx2…

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Q: Use the Jacobi method and Gauss-Seidel method to solve the following system until the L¹-norm of Ax…

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Q: 4) If y = 2√√x - 2 tan¹ √x, then y = 1 + x² * -1

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