A clamped cubic spline S(x) on interval [0, 2] is defined by 1+ax + bx2 – 2x³ 0

Q: . Let h(x, y) = x*-2xy²+2y²+7x? ) Find all critical points of h and at each critical point,…

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Q: 3. Find the maximum and minimum values of a 1 āz - on |z| ≤ 1 (where a with la| < 1 is fixed)

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Q: For u(x, t) defined on the domain of 0 <x< 2n and t 0, solve the PDE, a?u a?u a*u +t + cos(2x) +…

A: Given: To solve: ∂2u∂t2 = ∂2u∂x2+ ∂4u∂x4 + t + cos2x +sinxcost

Q: Xn Xn=3-(-1)" Xn = cos (¹) √1+n² Xn= 2n-5 Xn = where (yn) is bounded 4 Xn = n(1 + (-1)") + n ¹((−1)"…

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Q: 5. A clamped cubic spline S on [0, 2] is defined by So(x) – 1+ Ar + Bx - 23, 0<x < 1, S(x) – S1(x) –…

A: Using the conditions of cubic spline,

Q: 3. Solve the following initial-boundary-value problem by using the separation of variables…

A: Consider the 1-dimensional wave equation, when and with the boundary conditions, and initial…

Q: Suppose that Yt follows the stationary AR (1) model LaTeX:…

A: Given that Yt=2.5+0.7Yt-1+εt                         1  with Eεt=0 and Varεt=9 The standard ARt…

Q: If yı is a known nonvanishing solution of y" + p(t)y' + q(t)y = 0, then a second solution y2…

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Q: 2) Let y = c,x + C,x ln x be the general solution to x'y" – xy' + y = 0 on(-∞,). Find c, and c, such…

A: Given that the below equation is a general solution of x2y''−xy'+y=0. y=c1x+c2xlnx To find the value…

Q: 2. Find a general solution to the PDE du = k- êt with the given boundary conditions u(x,0) = 6 sin L…

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Q: 3. Prove that, if u (x, t) satisfies Ut for 0 < x < 1, 0 <t < to, then the maximum value of u is…

A: The given problem is to the maximum principal of heat equation for the given boundary conditions.

Q: 2) Suppose that a is a constant and {y1, Y2} is a set of solutions to the DE (1 – a2) y' – 2xy +a (a…

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Q: 6. Let u (x, t) be the solution of the initial-boundary value problem U = 0 0, Uz (0, t) = ux (4,…

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Q: 1. A function f(x, y) is homogeneous of degree 7 in x and y if and only if , 2. The function f(x,…

A: Topic:- calculus

Q: 1. A function f(x, y) is homogeneous of degree 7 in x and y if and only if, 2. The function f(x, y)=…

A: We have to find degree of homogeneous function

Q: Find the largest t-interval such that a unique solution of the following initial value problem is…

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Q: Consider the finction f(x, y) = 6y² + 4x² – 12xy- 4y. Then: (1,1) is a critical point and f has a…

A: The given function is f(x,y)=6y2+4x2-12xy-4y

Q: 5. Determine a function v(r, 0, ø) with Av = 0 _in B2 \ B1 satisfying the boundary conditions v(1,0,…

A: Use the cylindrical coordinates to determine the value of r. Now use the boundary conditions to…

Q: If the Wronskian of the three functions ex v is equal to zero, then the function y satisfies the DE…

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Q: Solve the following initial-boundary-value problem by using the separation of variables technique:…

A: Given :             utt=uxx                0≤x≤1   ,   t&gt;0 u0 ,t =0  ,u1 ,t =0…

Q: Find solution of an equation x X f(x) 1 1.0000 1.25 0.8000 1.50 0.6667 0.5714 1.75 2.0 0.5000 Using…

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Q: f(x) = 3 x4-4 x3-12 x2+1, has local minimum at x = %3D A O 1 .BO -2 .CO 2 .D O 0.

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Q: Show that the solution of initial value problem: d^2x/dt^2 + w^2x = F0cosAt, x(0)=0, x'(0)=0 is…

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

Q: Xn Xn=3-(-1)" xn = cos (¹₂) √1+n² Xn= 27-5 Xn=¹ where (yn) is bounded 4 lim inf(x) lim sup(x₂)

A: We know the fct that for every  bounded  sequence  limsup(xn) and  liminf(xn) exists finitely. since…

Q: 1. Use the separation of variables method to show that the solution of the heat conduction a’u du…

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Q: 2. Let f(2) = 2°e* z + 0. What type of singularity does f(z) have at z 0? (Justify.) What is the…

A: the point z=0  essential singularity.

Q: 3. Construct a suitable Liaponov function of the form ax + by and use it to determine the type of…

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

Q: 3. Find the residues of the functions 1- cosz а.) b.) c.) z'e at z=0; .5 e -1 and express the types…

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Q: Determine the largest interval (a,b) for which Theorem 1 guarantees the existence of a unique…

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Q: 1 7. Let f(z) = z2(ez+1)' a) Find all isolated singularities of f and their residues. b) Evaluate…

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Q: 1.6 Evaluate the line integral f x*dx + xydx where C is the triangle with vertices at (0, 0), (0,…

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Q: If y(t) solves the IVP dy = y2021 y2019 y(2021)= -2019, dt then lim y(t) is: t- 00 Oa. 1 O b. 00 O.O…

A: Given differential equation is dydt=y2021-y2019.       ........1 It is an autonomous differential…

Q: find the suprimum, in! infimum maximum and minimum of { c,1": (1+):ne w}, if t)ine w}

A: Supremum: Let A⊂ℝ then, least upper bound of the set is called supremum  of the set A. Supremum may…

Q: 3. Compute x In x da both analytically and numerically. Use trapezoidal, Simpson's 1/3, Simpson's…

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Q: Note that g(x) = čx² 3 + 6x + 6 on the interval -4 < x < 0 and that g(x) is a piecewise-linear…

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Q: IV. Let h(x, y) = x*-2xy'+2y²+7x? (a) Find all critical points of h and at each critical point,…

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Q: 26.Show that if p is differentiable and p(t) &gt; 0, then the Wronskian W(t) of two solutions of…

A: Given: [p(t) y′]′ + q(t) y = 0 W(t) = c/ p(t)

Q: 4.2) Suppose you wanted to find the absolute extrema of f(x, y) = ax² + bxy+cy? + dx + ey on the…

A: The given function is, fx,y=ax2+bxy+cy2+dx+ey We have one critical point on the rectangle,…

Q: 3.2 Let f(x) = Approximate the integral x4 x L f(x) dx using the Trapezoidal rule with n = 4. -2

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Q: 1.Suppose that the joint p.d.f. of Y, and Y, is defined by: e-Y1/y2 · e-Y2 0 < y1 < 0, Y2 0 < y2 < ∞…

A: Given: The joint p.d.f of Y1 and Y2 is defined by:

Q: Suppose that r1 and r2 are roots of ar2 + br + c = 0 and that r1 ≠ r2; then exp(r1t) and exp(r2t)…

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Q: Solve the problem with Neumann boundary conditions, 0, x, t>0 u, – Ugg = u(x, 0) = f(x) u;(0, t) = 0…

A: we have ut=uxx ux,0=fxux0,t=0 Fcut=Fcuxxdu¯dt=-su⇒u=Cse-s2tNow, ux,0=fx⇒us,0=f^cs=Cs⇒u=f^cse-s2t Put…

Q: For u(x,t) detined on the domain of- o 1 u(x,0) = Plot the solution, u(x, t), as a function of x at…

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Q: A clamped cubic spline for a function f on 0,3 is given by [1+ax² -2x', S(x) = . [1-2(x-1)+b(x-1)² +…

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Q: 1 Find skewness and kurtosis for the RV X with PDF f(x) = 2T -∞ < x < x.

A: PDF of X,  fX(x) = 12πe-x22, -∞&lt;x&lt;∞ So, μ = E(X) = ∫-∞∞x f(x) dx=∫-∞∞x 12πe-x22 dx=0 [as…

Q: Given an IVP d"y dz" dn-ly +...+ a1 (x) dy + ao (x)y = g(x) dr an (x) + an-1(x) dzn-1 y(20) = Yo,…

A: NOTE: Refresh your page if you can't see any equations. .

Q: 1. For u(x, t) defined on the infinite domain of -o 0, solve ди with boundary conditions: u(x, t)…

A: Given ∂u∂t=-∂4u∂x4+e-x2-t Boundary conditions: u(x,t) and its first and second derivatives in…