Example 9: use Trapezoidal rule to approximate S,(x³ + 3)dx; n= 6, then %3D compare the result with the exact value and find the percentage of error.

Q: e) On average, how far off is the model away from the true values?

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Q: 3. Find the average height of a point on the semicircle y =4- x over the interval -2 < x S 2.

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Q: hp (fh. Solve yda = (x - Vay) dy %3D

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Q: Using Euler's Method, approximate the initial value problem for various values of x given in the…

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Q: [+]。 + y² = 0 Ans:Order3 degree2, ordinary, non-linear d³y (4) +4 dx3

A: Given differential equation is d3ydx3 + 4dydx3 + y2 = 0

Q: 2.8 S = | f(x)dx =?

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Q: 1 By using completing the square , dx can be rewritten as /x²-4x – 7 1 VTr- 2)²– 3 1 =dx V(r- 2)? +3…

A: We need to write the following integral by completing the square   ∫1x2-4x-7dx

Q: Consider the following. Rx) = - 18x? 4 Ix4 - 18x2 %3D Find all relative extrema. (If an answer does…

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Q: H-wlo Find the dliscontinnity point of &cz):

A: Since you have posted multiple questions. I am answering the first one. Please post the question…

Q: Part 1 of 5 To find dy = y' for 9x3 + x²y – xy³ = 1, we differentiate both sides of the equation…

A: Answer is 0 Explanation is given below..

Q: Using Euler's Method, approximate the initial value problem for various values of x given in the…

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Q: Using the Trapezoidal Rule, an approximate value of 5 V(x + 3x)dx with 5 ordinates, correct to one…

A: Consider the given integral.

Q: Question 5 Find the value of df/dx at x = f(a). f(x) = x - 3x + 5; a = 5 1.

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Q: Using Monte Carlo, estimate the value of e*y dx dy. 0.

A: Given that, ∫01∫01exydxdy By the monte carlo formula, ∫01∫01exydxdy=∫01exyy01dy=∫01eyy-1ydy

Q: Solve this problem in digital format (Not by hand) step by step Solve the initial value problem by…

A: By the method of Separable of Variable

Q: 11. Do not use a calculator for the following problems. 3 j. a. Estimate |x*dx using the trapezoid…

A: Consider the integral  ∫03x2dx

Q: Q3\ Solve the problem minimize * J[y]= [[v +y"- 2y dx ,subject to the conditions y (0) =1 and y(1) =…

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Q: Using Euler's Method, approximate the initial value problem for various values of x given in the…

A: Let us approximate the initial value problem for various values of x given in the table using…

Q: -3 dx 1. Use the Simpson's and Trapezoidal rule with n = 4 to estimate Then compare the two results.

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Q: 4.2 Apply the appropriate method to calculate the following: x5+ I = S = s** dx x2 -4

A: Given  I=∫x5+x4-8x2-4 dx

Q: Using Euler's Method, approximate the initial value problem for various values of x given in the…

A: The given differential equation is dydx=9x2-4x+5,  y(-1)=0 To use Euler's method to approximate the…

Q: 3.2 The value of e-0.5*dx by using three-segment trapezoidal rule is most nearly 1.1

A: The complete solution is in given below

Q: The distribution of P(x,y) on a thin metal plate is given by ²P 2- dx2 = 0 ду? If we use a step size…

A: Given: Distribution of Px,y on a thin metal plate is, 2∂2P∂x2+∂2P∂y2=0 Step size: h=14, k=12   To…

Q: Use Euler method to approximate the value of y(2.2), given               ay' - by = cx2 + dx   ,…

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Q: Find the order and degree of 1 d y 1+ dx3 d'y dx4 O Order=3, Degree=20 O Order=4, Degree=20 O…

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Q: PART B: Find the Orthogonal Trajectories of the given family of curves. 8. y = c²(x² + 4y²);

A: Given curve is: y4=c2x2+4y2 To find the orthogonal trajectories of the given family of curves. From…

Q: While evaluating the approximate value of x2 dx, using Trapezoidal rule, taking 3 h = 0.5, the value…

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Q: 7

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Q: PART C: Find the Orthogonal Trajectories of the given family of curves. 7. x = 3(y – c);

A: Here we have to find the orthogonal trajectories of the given family of curves.    x3 = 3(y-c)

Q: What happens to N(t)=100x e^(5t) as t → infinity? Based on your answer would you consider this a…

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Q: Using Euler's Method, approximate the initial value problem for various values of x given in the…

A: Given differential equation is dydx=9x2-4x+5,     y(-1)=0        step size h = 0.2 initial values:…

Q: Question 1 Prove that 4 = ucy)e is a Solution for d24 - y°4 = 0 dy?

A: Given differential equation is d2ψdy2-y2ψ=0         (1) We have to check ψ=u(y)e-y22 is the solution…

Q: While evaluating the approximate value of x2 dx, using Trapezoidal rule, taking h = 0.5, 3 the value…

A: Given integral: ∫36x2dx h=0.5 To find: the value of N=?? [no.of sub-intervals]

Q: What is the numerical approximation to -dx -1 2+x using the basic trapezoidal rule? (a) 0 (b) 2 (c)…

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Q: The max value of y=sin x is a.1 b.0 c.1/2 d.2

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Q: The data below were collected by a chemical engineer. Y is filtration time, x_1 is temperature, and…

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Q: Find the values of "a" such that f(x,t) = e ax + 6t satisfies the equation of 2f ot dx? smallest…

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Q: 1 If the approximate value of dx is 0.2178 by Trapezoidal rule, then the error is 5x+7 а. 0 b. 0.369…

A: We will find error by finding the difference between exact value found by integration and…

Q: Using Modified Euler's Method, approximate the initial value problem for various values of x given…

A: Given y′=9x2-4x+5, y(-1)=0 , h=0.2, y(1)=?Here, x0=-1,y0=0, h=0.2,…

Q: Q1) Draw the graph of output power versus efficiency of transformer? Q2) Draw the diagram for…

A: 1. η=output power  input power=output power  output power+lossesη=output power  output power+iron…

Q: How do you find the local max and local min of this problem?

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Q: Find an upper bound for the error in estimating (5x3 + 2x)dx using the Trapezoidal Rule with n = 10…

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Q: Using Modified Euler's Method, approximate the initial value problem for various values of x given…

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Q: (a) Use n = 6 subdivisions to approximate the value of Vx + 3 dx by the trapezoidal rule.

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: dy dx3 y (0) y' (0) 1 y" (0) = 0 || ||

A: Introduction: The differential equation of the form D3+aD2+bD+cy=fx is third-order linear…

Q: Prove the reduction formula S x"e*dx = x"e* – n S x"-'e*dx

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Q: (15pts) Identify (write down) the type of DE, and find the general solution. (y- 3x)dy = (x +3y)dx…

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Q: 4 Use global extrema to find constants m and M such that m < dx < M. x3-2 1.5

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Q: Example 10.33. Applying Euler's method to the equation dyldx = Ay, given y(x) = yo %3D determine its…

A: Here, we need to use Euler's Method to solve given problem.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.