:Evaluate , V1 + x dx using Gauss-Quadrature formula (n=4).

Q: Find and at the given point without eliminating the parameter. x = Vi, y = 21 + 309; † = 1. dy

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Q: Q4) find the soluation of differention equation using exact equation 1) (1 + x²)dy+(2xydx)=0

A: I am attaching image so that you understand each and every step.

Q: Given f(x, y) (8a®y + 3xyf). Compute: dx?

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Q: Consider the two quadrature rules 0 Which one is better? Þƒ (¹) +cf (1), 2 3 + ߃ ( ¹² ) + yf าร์ (…

A: The function f(x) is integrated from 0 to 1.

Q: Evaluate the Ś Ŝ (x²+2xY+ y% ) dy de when Step Size of xz0.2 and step of y=o.5 ? (use -> Trafezoi…

A: let f=∫01∫02x2+2xy+y2dydx with step size h=0.2 we have x0=0.2 , y0=0.5 fx0,y0=0.22+2×0.2×0.5+0.52…

Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule t 10 In(x) dx,n = 6

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Q: What is the numerical approximation to 1 3 -dx -1 2+x using the basic trapezoidal rule? (а) 0 (b) 2…

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Q: H.W p.564/ use Trapezoidal method and Simpsons' rule to evaluate. dx 1) So √1+x² n = 4 se as Ars

A: # as per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: Evaluate e* dx dy by using trapezoidal and Simpson's rules.

A: Hello. Since your question has multiple parts, we will solve the first integral by first method for…

Q: Which of the following formulas would be used to calculate the trapezoid approximation of f2 dx…

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Q: Use the attached equation to find  dy/dx for this: 5tan−1(x2y) = x + xy2

A: Given, 5tan−1(x2y) = x + xy2

Q: What is P,(y) if the given DE is xydx – (3y – x²)dy = 0? %3D Select the correct response:

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Q: Evaluate e*y dx dy by using trapezoidal and Simpson's rules.

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Q: dx Evaluate J, +6x+10 by dividing the interval into 8 equal parts by using Trapezoidal rule.

A: The integral ∫15dxx2+6x+10. We have to evaluate this integral by dividing the interval into 8 equal…

Q: (a) Approximate the value of dx, using two and three points Gauss Quadrature Vx+A A: O

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Q: dz Find- at t = n, if x=21sin' 12t + 170, z=19cos12t +190t . %D dx

A: The value of sin (npi) = 0 We will put t=pi in dz/dx

Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

A: we know that lnmn=lnm+lnn similarly, ddxlncx=ddxlnc+lnx=ddxlnc+ddxlnx…

Q: |Q3/ By using definition, proof that d cot x dx - csc? x.

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Q: dx J. (3+x²)$/z

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Q: Use the trapezoidal rule to find A- using the indicated value of n. dx; n = 8 3 3x +3 A, = (Round…

A: We will evaluate the integral by using trapezoidal rule as shown below

Q: Given: y = sqrt(u)  ,  u = 2x2 + 3x + 4 Determine dy/dx at x = -3 a) Using Leibniz Chain Rule b) By…

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Q: Vx +1 dx x + 2 (b)

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Q: Find the linear approximation at x=0 to 1/(sqrt(2-x). Write your answer in the form y=Ax+B.

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Q: dy = Solve 2xy r x2 + y? given that y = 0 at a = 1 %3D

A: To find particular solution of D.E.

Q: Given y = Vx3 + 1, evaluate dr using delta process.

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Q: f (x) = 0, %3D pendently selected, find the E

A: The number of sample is n=4. a. The probability of impurity weights exceeds 0.5 is,…

Q: If y= Vx (x-1), find dy (Use rules, not a XP de finition

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Q: Find for the following by using appropriate rules: dx i. y = Vt , x: X = t+1

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: Evaluate J by means of trapezoidal rule using n = 10 and n = 20: 1 J = exp(-x²)dx = Se

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Q: Is this 2-form exact? w = x dx A dy

A: Given that ω=xdx∧dy To check this  2-form is  exact or not.

Q: In the following exercises, integrate using the indicated substitution. 361. 1. / 3 / + 1 dy; dy; u…

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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: Sahving DES with Homagoneaus Coafficients 2 (2724 y?) dz- xydy- o esson:

A: Rearranging 2(2x2+y2)dx=xydydydx=4x2+2y2xy       =4+2y2x2yxLet…

Q: The approximation of x'e"dx by Gaussian Quadrature with n=2 is (Use c21 = C22 =1 and r21= r22

A: Given :                 I = ∫01xeexdx

Q: Given z = 1le lle*y® , find 10 dz dz dy

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Q: the fact tbot E andL ofther,. L(x), 「ヘve-ses are Lbe)ミ1ax using of ench ofher, the formula well…

A: Given : E(x) and L(x) are the inverse of each other

Q: Given that y=ax , find dy/dx

A: To find the derivative of the given function

Q: Solve the diferential eguation with discasfssic Of soaL (4xy-y2) dx +(2x? - 2 xy + 2y?) dy=o

A: Given the differential equation is 4xy-y2dx+2x2-2xy+2y2dy=0 This is form exact differential equation…

Q: @ Consider the DE, dx %3D dt x (2t -7) What meho can be uoed

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

Q: dy Given that y = In 9x, find dz dy

A: Use derivative rules to find dy/dx

Q: find the dy リ=(メ+z)mx, (xを when 3In X

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Q: Use Composite Trapezoidal Rule with M = 4 to find: Lif(x)dx where f(x)=(1+x?)-1 Select one: O a.…

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Q: Find the extremum of f(x,y) = 4x²y2 +3y? + 5x?. %3D Answer:

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Q: Suppose f(5.25) = f(5.75) a. Find a if the composite Trapezoidal Rule with n 2 gives the value 12,…

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Q: Use the equation e = 2xyz+1 to find %3D az/əx and əz/ay.

A: We have to find

Q: Use the trapezoidal rule to find A, using the indicated value of n. dx; n=8 3 X +1 .....

A: Please refer the attached image for complete solution. THANK YOU.

Q: Express in form y=f(x) by eleminating the parameter x = e−2t , y = 6e4t

A: Here, x=e-2t and y=6e4t

Q: π ,t<. 3 b) Let y(t)= 1? + sint , find L(y(t)) 3

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Q: TT Find I = J? = Jó COs X dx 2 With trapezoidal method and n = 4

A: The integration can be approximated using the trapezoidal rule. The formula for the trapezoidal rule…

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.