QUESTION 4 The minimum value of n required to approximate dx by composite Trapezoidal rule xe with an error less than 0.1 is 0 4 O None of these 0 5 0 3.65

Q: Question 9 Determine the value of: xeª dx O 1/e e 2/e 1

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Q: QUESTION 3 dy = 2x+1. dx a) Find y at point (2,2), if

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Q: Question 7 2²e"² sin(x²yz) Let f(x, y, z) 12 find dyəzə"x at the point (3, 0,0) 4 8.

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Q: QUESTION 3 (a) Use the trapezoidal rule with 4 ordinates to estimate the value of x + In (2x) dx,…

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Q: Question 12 If the solution to e2x sec2(e2x+1)dx is equal to ktan (e2x+') + C, find the exact val S…

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Q: Question 18. Consider the function g(x) = sin² x, in the interval [0, ¤]. Use the Trapezium Rule,…

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Q: Question 2 Find dy at x=0 for each part below. dx x sec (ax+) a) (here the answer should be in terms…

A: NOTE: Since you have posted multiple questions, we have solved the first question for you. If you…

Q: Question 7 10 fx)dx into To use Gauss quadrature formula we have to convert 2.5/2.5+7.5x) dx 7.5…

A: Given: The integral  ∫510f(x) dx

Q: Solue the Following intial value problem cos?(y)dx + tany dy=0, y(1) = 0

A: Here equation is, xcos2(y)dx+tanydy=0 xcos2(y)dx=-tanydy xdx=(-tany/cos2y) dy

Q: Question 19 d'y If y = x In x, find dx2 A) -1/x B -1/x2 1/x2 D 1/x

A: Product Rule of differentiation : d(u.v)dx =u.dvdx+dudx.v d(xn)dx=nxn-1 d(lnx)dx = 1x

Q: QUESTION 2 16х + 7 Solving the integral /. dx yields: бх2+х— 12 )3 In(2x+3) + –In(3x – 4) +c a.…

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Q: Question 15 Let w = x'+ V9x, y= w°. Find ay dx

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Q: Question 5 The Integrating Factor for the DE y dx = (ye-2x)dy is 2y -2y None of These

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Q: dy .2 +3x² = dx 6x, y(0)=3 with step size a) Ar=1 b) Ar = 0.1 %3D c) Ar = 0.01

A: We can solve this problem by Euler's approximation.

Q: Question 4 a. Solve the following definite integrals. xp (* + x^€) ,'J (V&+1)* dx

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Q: Question (1): Let f(x) = 2x* –- 3x³ + 5x + 1. Find the value of at x = 1. dx

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Q: Cosinder the following initial value problem (IVP): y′ = 1 + x sin(πy), 0 ≤ x ≤ 1, y(0) = α + β (a)…

A: Existence and Uniqueness of Solution: Consider the IVP :  dydx=f(x,y) ,   y(x0)=y0 Then, (1) if f is…

Q: Question 10 of 10, Step 1 of 1 dy Find dx Answer for the equation below. dx 11 8/12 Correct 4x4 +…

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Q: Question 13 bx a dy dx 0.

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Q: Question 3 6x³e**3 dx. using integration by parts Svdu) and letting = UV u= f(x), dv= 3 g(x) dx,…

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Q: QUESTION 5 The approximation of x e*dx by Simpson's Rule is 0.160602 O 0.160603 O 0.162402 O None of…

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Q: Question 6 af Given f = esec (#) -ya+y, find dy (#) sec² (=) ye NO -y+In (y)

A: Given :f=esecxy-yx+y

Q: Question 2 Find the solution to the Bernoulli Equation. (3siny - 5x) dx + 2x²cotydy=0

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Q: dx

A: Given integral is We will integrate it by parts. Now, we know that

Q: QUESTION 4 Let G() = Jtan (x)dx_ Find 18G(1) + 140G'(1). %3D O A. 0 O B. 357 OC.No Answer is correct…

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Q: Question 3 Differentiate: y = arccot (x)+ arctan 01 O (E) None of these Ⓒ2x O 1-2x O < Previous 1-2z

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Q: Question 7 By algebraic substitution, the integral dx dx is converted to: 4+/x dy A) y+4 ydy B Jý+4…

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Q: Question 11 of 20 2 Po Solve (2x-y)dx + (x-1)dy=0 Select the correct response: NONE y+2 In a+ 1+ + C…

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Q: QUESTION 9 The solution of the IVP: = 2x+ dx? %3D y(0) = 2 v'(0) = 4 is y(x)= * +2 x sin-x + V1-x²…

A: Initial value problem is an ordinary differential equation having initial conditions on a specific…

Q: QUESTION 1 Solve the following first order pde by the method of characteristics: du at du + X = 2xt…

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Q: dy = Vx, y(0)=1, over the interval 0<x<4 with step size dx a) Ar= 0.5 b) Ar = 0.1

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Q: 4G OMANTEL l. moodle.nct.edu.om a Dashboard / My es MATH1200 citk 9. cours with Confidence T Self…

A: dy/dx=(dy/dt)/(dx/dt).

Q: If y=tan(arcsec/x), then dy/dx is sec2(arcsec/x) A 2х sec2(arcsec/x) (B © none of the given choices…

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Q: Question 5 4x2 Calculate the integral: dx 5+ x² V5 + x² - 10 ln V5 2х + C (5 + x²) 32 V5 + x2 V5 2х…

A: Indefinite Integration

Q: QUESTION 5 dy If y=5sinu and u=4e%, then the value of Y dx 4cos(5x) cos(20x) • 20cos(4eX) 20cos(5eX)

A: To find this will use chain rule of differentiation If y = f(u) and u= g(x) then according to chain…

Q: Question 11 dy =cos (x+y) , use the substitutions dx To solve the DE A z=cos(x+ y); dz= - sin(x +…

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Q: dx メー8メナ25 は)

A: Given: Formula used:

Q: Question 9 Given f = xy² In (3y + 2x) + (xy)e* (ry), find dy

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Q: Problem 13.1. Calculate the follo gration by parts: (1) Sa sin(3r +1) dx. (2) Sa'e(3r+1 dr. (3) ſ…

A: Since You have posted multiple subparts questions.  As per our guidelines we will do the first 3…

Q: Question 6 a. Solve the following integrals: i. Scos x) sin (-) dx il. SeVI+e*dx

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Q: QUESTION 12 The integral dx can be evaluated using a trig substitution with x+3=2sine. x +6x+13 O…

A: You say to solve the question number 12. So , we will check the problem number 12.  And we will…

Q: Question 2 Find the solution to the DE. (y- x+ xycotx)dx + xdy=0 O xysinx = C+ sinx – xcosx O y=…

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Q: Question 9 z=cos y Using the substitutions the DE (3cos y – 5x) dx – 2x²tan y dy=0 reduces to dz= –…

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Q: Item 8 of 10 What is S P, (x)dx if the given DE is y(6y² – x – 1)dx + 2xdy = 0? Select the correct…

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Q: Question 13 The integral csc(0.5) dx is equal to A None of the given choices B2ln|csc(0.5x) +…

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Q: Question 8 dy The appropriate substitution to solve dx + In(x + 1) = x°y³ is %3D O y = vx O z = y? O…

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Q: dx

A: To Determine: Calculate the integral.

Q: Question 16 Find dy/dx at the glven point without eliminating the parameter, r=0 + cose and y=l +…

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Q: dy +y = 12 e?Xy dx %3D12€

A: Bernoulli's equation: A differential equation of the form dydx+Pxy=Qxyn for all natural numbers n.…

Q: Question 13 d?y of y = 4x dx' Find the 3. y" = 4 Eethis reapon

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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.