Find, giving appropriate C and k witnesses, the big-O estimate (i) ƒ(x) = log(6x5 + 7x4 + 2x² − 2) (ii) f(x) = 122 (iii)ƒ(x) = 22x² + 9x² + 16 - 8x (iv) ƒ (x) : = 7x7 +4x²+x 4x³+7x²-1

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A: We have to find general solution of the ODE.

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Q: A matrix A= -10 -5 -1 40 37 -12] 20 20 -7 4 1 1 Find a basis for Nul A: 1 reduces to 0 0 -4 0 -4 3…

A: A matrix  reduces to .Find a basis for .

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A: We need to solve the given questions.

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A: K=2To compute cluster centroids and the next partition.

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A: Given, be a number with decimal expression.For,

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A: We shall be using the fact that a^p-1 =1 mod p

Q: dz de 02 -13 where dz dt 11 Z + [] 2 2 %3*م and Z [2]

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Q: 5. Look at some decimal expressions of fractions such as 3 25 15 20 14 50 2 7 9 16 71 50 91 b…

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Q: i. For a convergent real sequence sn and a real number a, show that if sna for all but finitely many…

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Q: What information about a root of the function can be determined from the graph? 300 250 200 150 100…

A: We want to tell about the root of function using given graph.If f(x)=0, then we say function haa a…

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Q: Let f : R² → R be defined by f((x, y)) = 8x+2y + 2. Is ƒ a linear transformation? a. f((x₁, y₁) +…

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Q: Apply the eigenvalue method to find a general solution to the system: x' = 4x+y+4z y' = x+7y+z z' =…

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Q: write the Matrix exponential For to show why ett - fet o #* = [6* > ] O A = [1 2] 3

A: The given matrix is .

Q: Consider the functional Slu] = [₁² where A is a constant and y is a continuously differentiable…

A: To show that the term   in the expansion vanishes under the given conditions, let's consider the…

Q: Evaluate f 3xdA where R is the region shown. 3. 2 4 2 10 R 2 4. 0 R

A: We have to find the double integral of problem (4).

Q: 6. Find the inverse Laplace transform of the following: (assuming that inverse transform exists): 8…

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Q: (i) Show, using calculus (meaning do not simply use graphs) and the Fixed Point Theo- rem, that the…

A: As per the question we are given a function and we have to show that it has a unique fixed point,…

Q: 2. Let n₁,..., nk be pairwise relatively prime positive integers, and let n = n₁ ... nk. Recall we…

A: this is also famous known as the chinese remainder theorem

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Q: Use power series to solve the initial-value problem 31 2

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Q: Show that p (p(n)) ≤n/2, for n ≥ 2.

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Q: -6 -5

A: The graph is a sine wave with a period and an amplitude of 1. So, we can use the function  to…

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Q: In the previous part, you developed the Method of Disks for computing the volume of solids of…

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Q: Solve the initial value problem y" + 1xy' -4y= 0, y(0) = 9, y'(0) = 0.

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Q: can you write this on paper please

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Q: Quadratic Interpolation • a strategy for improving the estimate by introducing some curvature into…

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Q: In Exercises 1-14, find the characteristic polynomial and the eigenvalues for the given matrix.…

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