4. Given these data X 1 2 3 5 f(x) 3 19 99 Calculate f(4) using Lagrange polynomials of order 3. 7 291 8 444

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A: Note: The geometric series has to be 324, -108, 36, -12,....., Otherwise there will be no common…

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A: The problem belongs to the concept of L.L.P.

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Q: 0,−1), (2,1,0), (3,1,-1), (1,1,1)} spans. {(c²,0,1), (0, c, 0), (1,2,1)} is a linearly R³. y, z) €…

A: Let us consider the set S=1,0,-1,(2,1,0),(3,1,-1),(1,1,1) To check R3=span S that is to check,…

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Q: 5. z = yex+x Iny xey-y lnx

A: Solution : z=yex+xln(y)xey-yln(x) zx=∂z∂x =∂ ∂ xyex+xlnyxey-ylnx-∂ ∂ xxey-ylnxyex+xlnyxey-ylnx2…

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A: To find- Find the steady-state vector for the matrix below. 0.90.20.10.8

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Q: Lemma*: If z(x, y) = W+H, then xZx + y2y = (xWx+yWy) + (xHx + yHy).

A: Solution:

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Q: 4. Consider the matrix equation Ax = b where, A = a b 1 1 where a, b > 0. (a) When is A strictly…

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Q: ach of these algebra

A: Given that the London bus tour company function                            T(x)=-x2+50x-225 where…

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A: Given ode is ,                                                                   xy(1+xy)dydx = 1…

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A: The equation of the yz-plane is x=0.

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Q: Determine the two values of z such that the middle 58% of the data lie between the two z-values.

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Q: 4. ( i) Consider the function f(x) = x²-7x+12 x-4 a) Determine the key features of the function: i)…

A: (a) We have f(x) = x2-7x+12x-4 We know x2-7x+12 = x-4x-3

Q: 4. Being careful to allow for parts of the curve being both above and below the x-axis, determine…

A: Solution : Area calculation between the curves, y=x(x-4)(x-6) and y=0 Intercepts of cubic equation…

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Q: Example 12.32. Four jobs are to be done on four different machin es) of producing ith job on the jth…

A: Number of rows = 4 Number of columns = 4 Therefore the problem is balanced find the minimum element…

Q: Evaluate: (7-j3)ln(cosh(2+j5))

A: Solution : Formulas, coshx=e-x+ex2 lna/b=ln(a)-ln(b) ln(a×b)=ln(a)+ln(b) To solve,…

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Q: Suppose a,b,n are integers and n>0 s.t. 63a^5b^4=3575n^3, what is the smallest possible n. Explain…

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Q: 9.W.1 The Gram matrix of an inner product on R2 with respect to the standard basis is G = 1 2 -1 ].…

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Q: Evaluate [√x² + y² ds_ along the curve r(t)=(4cost)i+(4sint) j+3tk, −2π ≤t≤ 2a.

A: To find- Evaluate ∫Cx2 + y2 ds along the curve rt = 4costi + 4sintj + 3tk, -2π ≤ t ≤ 2π.

Q: x-1) 1/6(x+2) 16/3- (x+1) 1/2 x-1) 1/6(x+2) 16/3 (x+1) 1/2 x-1) 1/6(x+2) 16/3 + +

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Q: Example 35. Using th d²y satisfying the differential equation v(1) = 2. + y = x, subject to the…

A: Here we need to use finite difference mthod.

Q: A spherical tank of diameter 4 m is half-full of water (weight density = 9800 N/m³). Setup the…

A: Solution:-

Q: Evaluate the following definite Integrals by using Gamma or Beta Functions: x² So (1+x6) ³ dx

A: