. Test for an extremum the functional I[y(x)] = [(x»+ x² – 2y²3y')dx, y(0)= 1,y(1)=2 |3|

Q: One of the followings is a harmonic function O a. u(x,y)=(x' - y' – 2x+1), O b. u(x,y)=(x-y - 2x+1),…

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Q: 1. Consider the function : = f(x, y) = V16 – r - 4y2. (i) Find the domain and range of the function.…

A: Given function is z=f(x,y)=16-x2-4y2. Solution of (i): Square-root is defined only for non-negative…

Q: (A B Which of the following functions satisfy x²dy + y(x + y)dx=0 with y(1) = 1 ? 3x²y = 2x + y x²y…

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Q: B) [. •] Find a function f(t) with f(0) = 0, ƒ'(0) = 3 if 10 L{f"(t)} = S

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Q: Find and locate the absolute extrema of the function f(x, y) = 4x − 8xy +2y +1 on D = {(x, y) = R² :…

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Q: Pr. #1) Find the exact value of So f(x)dx using the graph of f below.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: x sinx dy find f dx for y √ (x−1) (x²+1) Evaluate (u² + 2u + 3)' (u + 1)du

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Q: Consider the IVP: 1 y"(t) + 2y'(t) + 2y(t) = 1², y(0) = y(0) = 0 (a) The complementary function yo…

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Q: What are the smallest one-sided Lipschitz constants and the smallest Lipschitz constants you can…

A: Given function are fx,y=−y, gx,y=1 and hx,y=y. We have to find the smallest one-sided Lipschitz…

Q: Using Beta function, show that dx 3- (b – x) (x – a) |

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Q: Consider the variable coefficient linear non-homogeneous ODE where and where u and are unknown…

A: The given problem is to find the values of u' and v' for the which the particular solution yp =…

Q: Find an antiderivative F(x) of the function f(x)= 6sinx / 12+cosx such that F(0)=1.

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Q: Calculate Rs for f(x) = 6 - x over ver [3,5]. R8 IE

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Q: -2 (x² - y²)²] Evaluate: S₁ S² P₁² dx dy x+y

A: Let's evaluate given double integral.

Q: The function def ined by y=Acos(In(x)) +Bsin(In(x)) d²y dy is the solution of the following DE: x²-…

A: True . i.e. the function defined by y=Acos(ln(x))+Bsin(ln(x)) is the solution of the differential…

Q: 8. Sketch the Domain of ƒ (x, y) = ln (1 — x² − y²). f

A: The argument of natural log function is always positive. i.e., The natural logarithmic function is…

Q: Q.3 Let the functions f:R R and g: R→ R be defined by f(x) = ex-1 - e-lx-1| and g(x) = (e*-1 +…

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Q: Which of the following statements is the derivative of x2 y3+ 2 x y² - y = x³ with respect to y? dx…

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Q: () Sketch : (1) y=Jx+1 (x OSISI Isxs2 (2) y=- (-x r<0 G) y= 0sxs1

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Q: 6. Use the Fundamental Theorem of Calculus to find the derivative. Sketch a graph for each region. 1…

A: .  Derivative using the fundamental theorem of calculus is    .Derivative using the fundamental…

Q: If z=xtiy where x and y are real, find the real and imaginary parts of:- Z-1 Z+1 ピージ (x+アア 2.xy…

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Q: f(x) = + In(x) exp(x) + exp(-x) herex e [1, 5]. Use 5 nodes to uniformly cut the interval [1,5] into…

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

Q: (i) / x(V - 4) da. (H) / z*e* 1. Find „4p-3r³+7 3 – x2, 0<x <1 0 <x < 1 2. Evaluate | f(x) dx, where…

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Q: 6.(5.2) For R[0,1] × [0, 1] evaluate the following. (1) I I: = SSP (xy)2 cos(x³) dx dy R (2) 1 =…

A: Step 1: Solution-(1)Given: For R=[0,1]×[0,1] I=∫∫R​(xy)2cos(x3)dxdyOur aim is to evaluate the given…

Q: 19ver. Find y as a function of x if a?y" – 7xy' + 16y = 0, %3D y(1) = –5, y'(1) = –4. y =…

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Q: |sgn(-2.4)|+sgn(-0.2) = 2 TO FO

A: Note: Since, you haven't mentioned which question you would like to get answered. Here, we are…

Q: b) Find the Green's function for the operator £y(x)= y (1) = 0. (x + y(x))* with y (0) finite and dx…

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