A Bezier curve is defined with 4 control points as bo {0,0}, b = {1,0}, b2 = {2,-2} and bz = {-2,-2}. Convert this curve in the form of cubic B-spline by computing the polynomials using its recursive equation. %3D

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Q: 8. Show that the one parameter family of curves y² = 4k(k + x) (k E R) are self orthog- onal.

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Q: Find the exact length of the curve. v= In(1 – x²). y 0 <x < 1 In(|3|) - 8.

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

Q: Find The curl of the divergence of the grad given = 3x²y374-4x³y² + 2x³vz²

A: given ϕ=3x2y3z4-4x3y2+2x3z2 find the curl of the divergence of the gradϕ

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A: Given  y=sin(πx)x0=0,x1=1/6,x2=1/2

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Q: For the given polynomial y a2x2 + azx³, determine a2 and az that will make %3D (1,3) a point of…

A: Based on trial and error method we will solve the the first equation.  As per the bartleby policy,…

Q: 2. Find the images of the mapping W= z2 of the line y = 2.

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Q: Use the Euler Lagrange Multiplier to find three positive integers x, y, and z that satisfy the given…

A: Solution is given below:

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A: What is Polynomial: A polynomial is a real valued function. It is an algebraic function that is…

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A: Let the curve be y=f(x) , Given, initial and final points of curve is a, f(a) and b,f(b)…

Q: find the orthogonal trajectories of the family ofcurves. Sketch several members of each family. y =…

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Q: Let (-1,(-1) = 2), (0, ƒ(0) = 5) and (1, f(1) = 6). Which one gives quadratic spline functions?…

A: Given, -1,f(-1)=2,(0,f(0)=5) and 1,f(1)=6

Q: 7. The following data is given: 3.4 3 2.2 4.8 2 2.8 3.2 4 5 (a) Write the polynomial in Lagrange…

A: Lagrange Interpolation formula f(x)=(x - x1) . . . (x - xn)(x0 - x1) . . . (x0 - xn)f0+(x - x0) . .…

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Q: 1. See the graph below. What is the degree of polynomials for this Bezier curve?

A: Given- To Find- The degree of the polynomial of the above Bezier curve.

Q: Use the numbers x, = 2 , x, = 3 and x, = 4 to find the second Lagrange interpolating %3D polynomial…

A: First of all we have to find the second Lagrange interpolating polynomial for f(x)=1/x Then we have…

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Q: Consider the data: 0 1 2 3 4 f(x) -4 -3 -2 5 12 a) Applying the Composite Trapezoidal Rule with all…

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Q: Show your work for each problem. For the data points (1,0), (2.0.693), (3.1.099), and (4,1.386): 1)…

A: Please upload the multiple parts separately.Here i answered 1st one i.e, (1) as per our policy.

Q: Which of the following statement is false about a quadratic spline with 2 knots? A. It has 5 degrees…

A: The question has been solved in step 2.

Q: 3- Determine the Lagrange polynomial that interpolates the data in the following table 2 4 y 1 -1 3…

A: From the given information, x0=0,x1=2,x2=4,x3=6 and y0=1,y1=-1,y2=3,y3=4. Formula for Lagrange's…

Q: Compute the interpolating polynomial through the points (–1, 5), (1, –3), (3, 21) using the…

A: Since you have posted multiple questions but according to guidelines, we will solve first question…

Q: Suppose the new quadratic g(x) = x + px + q has the roots y = a+B and & = + %3D %3D Find the…

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Q: 3. The vertices of AFGH are F(-1, 1), G(-5, 4), and H(-5,-2). X is the midpoint of FG, and Y is the…

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A: integration

Q: Find the total length of the loop of the curve 6y^2 = x (x - 2)^2 between x = 0 and x = 2.

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Q: A Bezier curve is defined by PO (0,0), PI (2,5), P2 (5,5) and P3 (7,0). Sub divide the curve at u…

A: We will get only one point as we have only one value of u. The given points are P00,0, P12,5, P25,5,…

Q: a. bisection method with x₁=0.5, x₁=2. ε = 2% .Regula Falsi with x₁=0.5, x₁=2. = 1%

A: Here follow the simple python script.

Q: 10) Use Lagrange coefficient polynomial L3,2(x) to find L3,2(5) using the nodes Xo = 3,x1 = 4, x2 =…

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Q: Determine the quadature rule of the form | f(r) dr = Aof(ro) + A1f(£1) + - *·+ Anf(Tn) a. when the…

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Q: Find the vertical. and harizantal Asyntotes of Cach Curve. 2ek

A: Answer

Q: b) Identify all intercepts. (If än änswer đoes hot exist, (x, y) = ( 0,0 (. x-intercept %3D…

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Q: QCx) = (x +s)? (x=3)4 %3D

A: Q(x)=(x+5)2(x-3)4

Q: Suppose that Pɔ(x) is the second degree Lagrange interpolating polynomial for the data: 1 2 Yi 3 6…

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Q: Construct the cubic B´ezier polynomial given the following points and guidepoints: point (1, 1) with…

A: Bézier curve as a polynomial instead of a sum of less straightforward Bernstein polynomials.…

Q: Find the exact length of the curve. y = In (1 - x2) ,    0≤   x ≤ 1/2

A: Given, y=ln1-x2,0≤x≤12 We know the ars length formula is, L=1+dydx2dx Now we find the derivative by…

Q: Find the points on the graph of z = xy + 8y-1 where the tangent plane is parallel to 6x + 5y + 6z =…

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Q: calculate x, , X2, Xg from the foloueng ノ equations using Gauss E limination method 一 3X, + X2 +…

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