Find the difference c-d for the following cubic spline S) with natural boundary conditions: S(2) = { Sa(z) =1+2z + 2r", 0

Q: Q#9) find the clamped cubic spline that interpolates the data ( 1,–1), (3,22), f'(1) = 0,f'(3) = 24

A: Given data: x f(x) f'(x) 1 -1 0 3 22 24 To find the clamped cubic spline that interpolates…

Q: 4. Find the maximum and minimum values of the function f(x, y, z)-x+y-z over the sphere x² + y² +…

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Q: 5) Let z, and z, be two non real complex cube roots of unity and |z – z| + |z – z3ľ = 1 be the…

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Q: C) lie in the parabola 16y = 160 – x². Find the maximum area of the triangle if side rtices B and C…

A: Sol

Q: [(x²y + Dinx) dy C is the arc of the parabola Y=x² from (0, 0) to (71, 71²)

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Q: Determine the values of the coefficients a, b, c, d, and e so that the following f(x) is a natural…

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Q: Find f. (12z + z?) dz, where C is the boundary of the rectangle with vertices at the points 1+2i, –…

A: As you have asked more than one different question, we shall solve first question only. For others,…

Q: In a cubic spline approximation assume that we know that S;(x) = 4 – 5x+ 2x² + 3x³ Si+1(x) = a + bx…

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Q: Ex.7 The area of the surface ∑ = {(x,y,z) €R® : (x² + ²) < 1, z = 9 + xy} is: (A) - 5 (B) 4개 2 (C)…

A: Using polar coordinates.

Q: Shade the area of the region bounded by the parabola, x² +p² – 2(p + 7)x – 5y + 59 + 14p = 0 and the…

A: We rewrite the equations  of parabolas and straight lines with p=9 as…

Q: Find the equations r = g (0, z) (cylindrical) and p = f (0, 4) (spherical) for the hyperboloid x² =2…

A: To find-  Find the equation r = gθ, z (cylindrical) and ρ = fθ, ϕ (spherical) for the hyperboloid…

Q: fj+1 - fj-1 2Ax Assuming a uniform grid spacing of Ax, derive a finite difference approximation to…

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Q: 2. Let l be the line x² + y² − 4x + 2y +1 = 0 and drop a perpendicular from O to Q E l. (a) Explain…

A: Step 1:Part (a): Finding the coordinates of (Q), where a perpendicular is dropped from the origin (…

Q: trapezoidal rule T t

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Q: Consider points P and Q in the x-y plane, with P = (1,0) and Q = (0,1). The line integral %3D Q…

A: The line joining P1,0 and Q0,1 is     x-11-0=y-00-1=t(say)⇒x=t+1,y=-t⇒dx=dt,dy=-dt

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: Minimal annihilator, L, of y = (x² − 2x + 1)e-²x

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Q: xux-yuy+y2u=y2x find the general solution

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Q: la). Show that f(x)=(x-2)² – Inx =0 has at least one root between 1 and 2. b). Use bisection method…

A: Since you haven't specified the part of question you'd like to be answered, so we have solved (a),…

Q: 4. Verify whether S(x) is a cubic spline x³ x - 1 S(x) = { ²² + ² 17²³ + 2(x − 1)² + 4(x − 1) + 1 −…

A: A function S(x)  is called cubic spline in  if S(x) satisfies the following condition.

Q: Find the best quadratic approximation, Q(x, y) of V9 – 6x – 4y for (r, y) near (0,0).

A: We have to find the best quadratic approximation Q(x,y) for (x,y) near (0,0).

Q: Let F(r, y) = (x + 1)7, and let C be the portion of the parabola y = x² that starts at (0,0) and…

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Q: Find the maximum value that f(x, y, z) = x² + 8y - z² can have on the line of intersection of the…

A: Given function is f(x,y,z)=x2+8y-z2 and the other constraints are g(x,y,z)=2x-yh(x,y,z)=y+3z We…

Q: Let V₁. Vk be the points in R³ and suppose that for j=1,..., k an object with mass m, is located at…

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Q: Q6: Find the residues of a) f(z) = Z² 2Z and (ZH)²(Z²+4)

A: Since you added two questions, find the solution of the first one.

Q: 5. If X any Y are sets, then X-Y= {r€ X: 1¢Y} If X is open set and Y is closed set. Prove that (a)…

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Q: In class Problems rol13 ) Find all real Gnd complex roots of: fa)= x*+ x³ - 8x-8 a function 2) Find…

A: According to guidelines, attempt only first question. If You want solution of another question then…

Q: Let q be a quadratic form on R, defined below with u = (r1, 12, 13). Find the rank and the signature…

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Q: Let a < c < b and s(x) be a cubic spline with a single node c. Suppose s(x) = 0 on [a, c]. %3D Show…

A: Let a&lt;c&lt;b and sx be a cubic spline with a single node c. Let us consider sx=0…

Q: Solve the problem. Find the point on the parabola z = t, y = t, -00 <t <o, closest to 9 3 A) ) %3D…

A: Here we will use the concept of maxima and minima. Since we will have to find out closest point to…

Q: Determine the value of the coefficients  a, b, c, d and e such that the following f(x) is a natural…

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Q: - For what values of parameter c, is the quadratic form (a) positive definite (b) positive…

A: The quadratic form Q(x, y) = 3x^2 - (5 + c)xy + 2cy^2 can be represented by a symmetric matrix A as…

Q: 1 P and Q are points on the sphere x² + y² + x² = 4. P₁ and Q₁ are the foots of two perpendiculars…

A: To find the maximum of the expression 2|PQ|² - |P₁Q₁|² - |P₂Q₂|², we need to analyze the geometric…