1) Find ôz|ôu and ôz/ôv for z= 4e* In(y), x=ln(ucos(v)), y=usin(v) at the point (u, v) = (2, 7 | 4). %3D Ans. Z, = v2(1n2+2), z, = -2/2(In2– 2)

Q: Let yn. a....Mo be a random sample from an exponential pdf with unknown parameter A. Find the form…

A: Let, y1,y2,...yn be random sample from the exponential pdf with unknown parameter λ. Now, to find…

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A:

Q: (2x+5)² 19. What should be the rewrite of the integrand of S -dx so that the resulting integral is…

A: Given query is to rewrite the integrand in integrable manner.

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A: Given that Φ(x,y) = ex-y and Φ(ln2,ln2)=1. Now by using the technique of linear approximation we…

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A: 3 classes of second order of PDE's based on the classification are Hyperbolic, Parabolic and…

Q: 2.) Evalvate the Integral ودل أاد-ل (x² _33² dx, .3 2 by making w - x²-3 NOTE: Answer should be in…

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Q: 10. Jljul * If µ(x, y) = x" y"is an integratingfactor of the the DE. (12 + 5xy)dx + (6x y + 3x²)dy =…

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Q: 6. Let a be a positive constant. Determine the general antiderivative of a using the fact 1 a² + x2…

A:

Q: 3 Estimate e2* sin(x) dx 1 using the Trapezoidal Rule with n = 1,2,4 and 8 segments 2) using Romberg…

A: Part (1): (a)The trapezoidal rule stats that:

Q: 1) y = 2sin (5x) ,2) y = In x'n cosh 5x ,3) xsin=14y = y tan-14x 4) y = ecosh (8x),5) y =- t +1 t…

A: As per our guidelines, we are supposed to answer only one question. Kindly repost other question as…

Q: Find the total differentials of w=2z2 ysinx

A: The detailed solution is given below Thank you

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Q: 1. Evalute the improper integral 3x dx. J ' 1+ x² -1

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

Q: The integrating factor µ(x) of the differential equation: dy (x In x) + y = 2 In æ is In x H(x) =…

A: Integrating factor is lnx see the step 2

Q: 8 2 1. Reverse order, then integrate Sr) dydx.

A: Given:    Intergral is given

Q: 4. Is y' = sin (ty) separable a) not separable c) separable %3D b) for y =, yes d) with a proper…

A: We have to check whether the given differential equation is variable separable or not.

Q: 3 Evaluate the integral: dx 2 Vx -1

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Q: Integrates PDE SE ニー Zく Z8 te

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Q: 1. Evaluate the integral 2 1-2 8x cos y dy dr y - 4 by reversing the order of integration.

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Q: Evaluate the integral: e3+cosh2x33+cosh2xsinh2x dx (Α) (3e)3+ sinh2x 2+In3 + C (3e)3+cosh2x B 2+2ln3…

A:

Q: Evaluate the integral: e³+ cosh2x33+ cosh2xsinh2x dx A (3e)3+ sinh2x 2+In3 +C (3e)3+cosh2x B) 2+2ln3…

A:

Q: 4. Use the Fundamental Theorem to evaluate (x³ - 6x)dx . (Your answer must include the…

A: Use the integral of polynomial.

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Q: integrals in Erarnices 6 to 20: dx 8. (ax +bx+c) dx 7. Vx - 1 dx (11 x' +5x - 4 dx dx 10. - dx…

A: Given :

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Q: Reverse the order of integration 3 Lütfen birini seçin: a. 1 √3 √316 b. 1 So C. e d. 2 e. √3x 2² v²…

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Q: 2(150–x2) 100+r 3x2 100- dt 300–2x2 100+1 3x2 100- dx2 di dx2 (5) (300–2x2)(100–1)–3x½(100+1) %3D dt…

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Q: 3. f(x) = _-x² +1_ %3D 9- x + zX Holes: Vert. Asy: Hor. Asy: x-int: y-int: Domain 4. f(x) = x3 – x2…

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Q: RT 5.2 Consider the differential: dp = dT + - ) dv (where a is a constant) (a) Determine whether the…

A: If we have dz=A(x,y) dx +B(x,y) dy, then, the differential is said to be exact if…

Q: 4. (a) Prove that M(x, y) + N(x, y) = 0 can be made exact using an integrating factor that = f(x+y)…

A: To find-  Prove that Mx, y + Nx, ydydx = 0 can be made exact using an integrating factor that…

Q: (2x+5)² 2. What should be the rewrite of the integrand of ſ x2 dx so that the resulting integral is…

A:

Q: 2 Evaluate the improper integral 4x e dx, if exists. 8.

A: Given that,           ⇒           ∫-∞2e4x dx   ,   if exist             ⇒         find the…

Q: 5. Find the particular integral of d²y + dy - x2 + 2x + 4 dx2 dx

A: We use the operator method to find the particular integral of the given differential equation.

Q: 4 In |x=3| The improper integral dx can be written as: x-3 Select one: 3 In(3-x) dx 4 In(x-3) dx a.…

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Q: Evaluate the integral: e3+ cosh2x33 + cosh2xsinh2x dx A (3e)3+ sinh2x 21n3 +C B (3e)3+cosh2x 2+2ln3…

A: This question can be solved using integration by substitution.

Q: 3. Estimate the integral v2 + x² dx using appropriate of Simpson's rule with step size, h = 0.2.

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Q: Consider the differential equation dy dy +2- + 4y = 0; y(0) = 3, dx dy| = 0 dr dr² Is this initial…

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Q: 1. Evaluate the integral 2 8x cos y dy dx y – 4 by reversing the order of integration.

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Q: 2. Integral A e3A dA

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Q: Show complete solution Expand, that is, perform the indicated operations on the differential…

A: To expand, that is, to perform the indicated operations on the differential operator, xDD+x

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.