Write A Short Note On Interpolation And Approximation.

Q: use some form of technology to determine the eigenvalues and a basis for each eigenspace of the…

A: A number λ is said to be an eigenvalue of the matrix A if there exists a non-zero vector x such that…

Q: Find the surface area of the surface given by the portion of the paraboloid z = x² + y² that lies…

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Q: if we reflect a point (x, y) about the x-axis and then take the result and reflect it about the…

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Q: II r ( 2 + ³ − ¹) = (2x) ² (M-1) (2x);(m−1) m’-mīr(mz) П S=l

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Q: For the function given below, find a formula for the Riemann sum obtained by dividing the interval…

A: We use the definition of the Riemann sum and then evaluate the expression for the given function. We…

Q: One Prove Property the flig statements property li is true by reordering to form a proof A, BV Max…

A: Given: A and B are in M3×3=V.To show: A⊕B∈M3×3=V by using the following statements, (A) Assume that…

Q: (a) Find a basis for the nullspace of A. Make sure you justify that it is a basis. (b) Find a basis…

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Q: 1. Find the equation of the conic whose only vertex has coordinates (-1/2,1) and passes through the…

A: Since the conic has only one vertex it is a parabola. This idea will be used to solve the problem.…

Q: 1. Verify that the following limits do not exist by finding two different paths approaching the…

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Q: Which answers are correct there

A: Let S be the relation from A to B. Then  S2 means S(S(A)) .

Q: ор (i) [0, 1) × (0, 1]

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Q: 35-8 12 7 16 31 4 -2 S 2 t-1 -2 3 = A rref (a) Find null space (6) Find a basis for the null space 4

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Q: Use mathematical induction to prove that the sum of the cubes of any three consecutive natural…

A: To show that sum of the cubes of any three consecutive natural numbers is a multiple of 9. Let us…

Q: 14. ↑ foo 1 15. 14.15 Draw fix) foo

A: Graph of the function fx is given, we have to graph its derivative function f'x.

Q: In GHI below, GI is 3.5 m and G is 33°. Determine the length of GH to the nearest tenth of a…

A: first see note for just reference.  problem1 , final answer is GH = 2.9 meters

Q: Show that the given function is a solution of the differential equation. d²y dx² Substituting +9y =…

A: To prove that the given function is a solution of the differential equations…

Q: = P2M2x2 by f(ax² + bx + c) = =f: P₂ a (a ² b b). a-c a+b

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Q: Problem 1. For the following, write down an example. No further justification is needed. Please be…

A: I have given the answer in the next step. Hope you understand that

Q: Find the image of a triangle whose vertices are A(2, 4), B(4, 2), and C(6, 8) under a dilation with…

A: Given  A(2,4), B(4,2)  and C6,8 Given dilation factor 12 where the origin is the center Therefore…

Q: . Use mathematical induction to prove each of the following: * (a) For each natural number n,…

A: (a). To prove that for each natural number n,                         2+5+8+. . . +(3n-1)=n(3n+1)2.

Q: Find the volume of the solid that lies inside both the cylinder x² + y² = 25 and the sphere x² + y²…

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Q: A tank contains 100 kg of salt and kg 2000 L of water. Water containing 0.3 of salt enters the tank…

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Q: Determine whether (-1). 7n³/2 n² + 2 n=0 yerges conditionally, or diverges. converges absolutely,…

A: Given series is  ∑n=0n=∞-1n·7n3/2n2+2. To Find : whether the given series is absolutely convergent ,…

Q: 16. 0 1 BOL 9 0 1 6 - 1 2 9 5 −3 3 -4 - - 9 3

A: Given Data: Let us consider the given data, 1001, -21-11, 6-12-1 ,5-33-4,03-11 To Find:  The basis…

Q: b) x²= x=tx²³

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Q: Answer T or F and justify your answers (a)* Under a translation, when one point of a figure travels…

A: This is a problem of Linear Transformation.

Q: Prove the following. 2. Let x, y, and z be integers. If rly and ylz, then x|z.

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Q: (a) Evaluate the following integral using the complex exponential: -2x Je sin(5x) dx

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Q: Which of the following infinite series con- verges conditionally? 1. 2 Σ 3. 4 Σ (-1)* 8k ln(k) + 6…

A: Given a series ∑n=1∞an . If the series ∑n=1∞an converges but the series ∑n=1∞an does not converge.…

Q: Find the present value of $90,000 due in 7 years at the given rate of interest. (Round your answers…

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Q: 15. Let a be a real number. We will explore the derivatives of the function f(x) = eax. By using the…

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Q: Relation Between Gamma and Beta Function : B (p, q) = r(p)r(q) r(p+q)

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Q: Find the general solution of the equation. x³ dx + y dy = 0

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Q: Suppose you buy  $3400 worth of furniture for a new house. The furniture store is offering a fixed…

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Q: T‐Talk cell phone company charges a flat rate of $15 per month plus $0.10 per minute in calls.…

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Q: T Let D be an ellipse rotated counterclockwise by radians, as pictured below. Before rotation, the 6…

A: It is given that the ellipse is rotated counterclockwise by π6 radians and before rotation, the…

Q: 5πT Convert the point (p, 0, ¢) = 3, π to Cartesian coordinates. Give answers either as expressions,…

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Q: A man is walking at a rate of 6 miles per hour towards the foot of a tower, 80 feet high. At what…

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Q: Verify that (¹)² = i²i but that (i²)i ‡ į²i ("i" imaginary unit)

A: What is Complex Number: A real number and an imaginary number are effectively combined to create a…

Q: Show that arcsech(x) = arctanh(√1-x²) where arcsech(x) is the inverse of f: [0, ∞) → R, f(x) =…

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Q: Part a: Set up an expression for the profit from producing and selling x items. We assume that the…

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Q: function f(x) = cos x cosh x +1 using the following methods. Determine also the relative approximate…

A: Given: fx=cosx coshx+1 , xl=1 , xu=2 To find the Root of function. Determine the relative…

Q: Show all necessary solutions and justify answers 1. Prove by Contraposition: Let n E Z. If n² is…

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Q: Find the centroid of the region bounded by y² = x +98 and x = 98, assuming the density 6(x, y) = 1.…

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Q: find a counterex for property 7 gives matrices A e Mzxz and BEM3x3 and scalar c So that C (A #B) #…

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Q: Use Euler's method with the given step size to estimate y(1.4) where y(x) is the solution of the…

A: Since you have posted a multi subparts question according to guildlines I will solve first three…

Q: A) B) C) Find using implicit differentiation. (No need to simplify your final answer. But should be…

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Q: A diagonalisation of a matrix A is given in the form P-1AP=D.List the eigenvalues of A and the bases…

A: A diagonalization of a matrix A is given in the form P-1AP=D. Here P-1=16161612-12-121313-23,…

Q: 10. P = $12,000, r = 7.8%, t = 45 days

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Q: QUESTION FOUR a Given that 21nx+1n3=In(5x+2). form px²+x+r=0 stating the values of p. q and r b.…

A: Properties of logarithmic function   ln ab=blnalna·b=lna+lnblna=ln(b)⇒a=b