21. Show that the set of polynomials {C₁, C₂ (2x - 1), C3 (6x² − 6x + 1)} in P(R) is orthogonal with respect to the inner product f f(x) g(x) dx for any choice of the constants C₁, C2, C3. For what values of C₁, C2, C3 is the set orthonormal?

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Q: Determine which of the following statements is true about the tableau shown below. BV P X1 X2 S1 $2…

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Q: 20. Twelve children are to be divided into groups of three to play different number games. In how…

A: Solution :- Given, Total no. of children = 12 We have to divide into the three groups.

Q: b) Prove or disprove: i. [x]-[x]. ii. For all positive real numbers x and y, [xy] ≤ [x] - [y].

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Q: 3

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Q: Use​ Newton's method to approximate all the intersection points of the following pair of curves.…

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Q: Classify each series as absolutely Convergent, Conditionally Convergent, or Divergent. (−1)k+1 6k ∞…

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Q: b) y"+y=0.

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Q: Exercise 5.100. Let C = {k,l,m,n} and D = {p.q, r, s,t}. Is there an onto function from Cinto D?…

A: The given sets are, C=k,l,m,n, and D=p,q,r,s,t. To Explain: Whether there exist an onto function…

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Q: Consider a cylindrical shell of constant density p, inner radius r₁, outer radius R, and height H.…

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A: Thank you for the question. According to our guidelines we can answer only  first question and…

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A: 1st we will make equation of 3 variable a,b,c using given data and then  solve it by cramers rule…

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Q: a) Solve the exact differential equation x-2 dy dx subject to the condition that y 1 4 -2x (x > 0)…

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Q: B = (!!) : (AB) = BA +₁+

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Q: 8. How many different boxes containing 10 wedges of cheese can be made by using wedges of Cheddar,…

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Q: √2+√6 √√2+√3 4 = by solving for cos (F) using (a) 12 1. Show that 2 sum or difference identities and…

A: We can show the given equation.

Q: Evaluate J sin(x + y)dxdy, R where R is the area bounded by the lines y = x, x+y= π/2 and y = = 0.

A: We can find the integral.

Q: (b) Find a basis and dimension of the vector space B-C J = where B U = {A € M22 | AB = BT A},

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Q: 2 Obtain a power series solution of the equation (1 + x²)y” − 3xy' – 5y = 0 - - up to and including…

A: Sol:- 1+x2y'' -3xy' -5y=0A linear homogeneous ODE with constant coefficients has the form of pxy''…

Q: ****- # PANKK 245 w (0 6**) jead 243 www. (**) 4 Find the length of the curve

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Q: First derivative of 2 F₁(x): d a.b {2F₁ (a, b; c; x)} = ªb ₂F dx C 2F₁ (a +1,b+1; c+1; x)

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Q: Given the initial-value problem: dy dt = 1- t + 4y y (0) c) 4th Order Runge-Kutta (RK4) Method = 1…

A: Given: The initial problem is given by:                                    dydt=1-t+4y…

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Q: = 7. Consider the set Seq[N] of all the infinite sequences (ak)ken = (ao, a₁, a2, a3,...) of natural…

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Q: State why the system of equations must have at least one solution. (Select all that apply.) 2x + 3y…

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Q: [4] Use Gaussian elimination with back substitution to solve the linear system of equations 4x1 − X2…

A: Sol:- Converting given equations into matrix form   4 -1 1   8     2 5 2   3     1 2 4   11…

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Q: c. Apply the principle of diagonal dominance and solve the system again. Use Gauss- Seidel with an…

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