Let {E} be a countable collection of sets of real numbers. Then UEn ≤Σm* (En) n * m n

Q: 1. Let A, B abd C be sets. Prove that Au (B-C) = (AUB) - (C-A).

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Q: j Find the general solution of the following ODE by reduction of order. Given that y₁ = is a…

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Q: 2 y = 0.38 sin x-.49x²

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Q: 1. Compute the average height of the cone z = a> 0. r² + y² above the disk x² + y² ≤ a² for

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Q: For all a > 0 and b> 1, the inequalities In (n) ≤ nº, n<b" are true for n sufficiently large (this…

A: We will write different version of inequality between ln(n) and n for sufficiently large n.

Q: Use row operations to solve the system. x+ y− z= −6 2x− y+ z= 6 x− 4y+ 3z= 5

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Q: 1 2 (FF3 √k + 3 1 √k +2

A: The given problem is to check whether the given series is converges or diverges and also find the…

Q: Romberg integration for approximating f f(x) dx gives R₂1 = then f(2)= -6 and R₂2 = 1

A: Given that Romberg integration for approximation ∫04fxdx gives R21=-6 and R22=1. We have to find the…

Q: Solve the equation COSX = X Mumerically using secant approach. Choosing Xo₂0 and X₁ = 0,5 =

A: The secant method uses the formula: xn+2=xn-f(xn)⋅xn+1-xnf(xn+1)-f(xn) to perform the iterations to…

Q: 4. A password to a vault must have at least 8 characters where each character can be an English…

A: It is given that password can be  English letter or a digit. So available characters are:…

Q: Q2/1 x = 0; pi/100 : 2 Pi; Y₁ = Sin(x) 2. Sin (X-0.25); 83 Sin (X-0.5); ун Y₁ = Cos (x); plot the X…

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Q: Consider the sets A = 0 and B = {0} and C = {1,0}. 5. Find each of the following sets, if it is…

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Q: 1 (In (n)) It is not possible to use the Direct Comparison Test to determine the convergence or…

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Q: Determine the values of a, if any, for which all solutions of the differential equation y" − (2a −…

A: This is second order differential equation, it has two linearly independent solutions, if both are…

Q: Let f be the function that contains the point (-1,8) and satisfies the 10 x²+1' differential…

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Q: (i) If A and B are two sets such that ACB, then m* (A) ≤m* (B).

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Q: 4. If fige Lim. 1/2 show that fy & LUTY.

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Q: Use the method of variation of parameters to solve the initial value problem x' = Ax + f(t), x(a) =…

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Q: Let R={(x,y) ERxR: |x| = |v|). Then R a function on R. оо True False

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Q: ute a fundamental set of solutions tal set of solutions of the differentia

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Q: Determine the measure of angle A where A: (1, -2, 4), B: (0, 5, 1), and C: (-2,3,0) in degrees.

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Q: Given the following initial-value problem: dy dt di² y(1.5)=1. y'(1.5)=1. Determine numerically the…

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Q: If the Wronskian W of f and g is t²e7t, and if f(t) = t, find g(t). NOTE: Use c as an arbitrary…

A: We have to find value of g(t)

Q: 1 Find the general solution to the following ODE using the method of undetermined coefficients…

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Q: Ex: Find the center of mass of the solid whose density &z and bounded above by the plane z=y, below…

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Q: Consider the model dP dt where P(t) represents the size of the population at time t. = 5P + 10P²,…

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Q: 4. Given that √2 is an irrational number. Show that 5+ 3√2 is an irrational number.

A: Solution 4 Here given that 2 is an irrational number  To prove   5+32 is an irrational  Proof Let…

Q: Given the following initial value problem. dy/dt- yt 1.1y where y(0) - 1 The solution at t 0.75; Le…

A: Euler's method uses the formula: yn+1=yn+hf(xn,yn) to perform the iterations and approximate the…

Q: At the beginning of each month, $200 is deposited into a retirement fund. The fund earns 6% annual…

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Q: If matrix A is invertible, then A admits an LU (or LDU) factorization if and only if there are no…

A: Proposition Let be k*kmatrix. If can be reduced to row echelon form by Gaussian elimination without…

Q: Solve the third-order initial value problem below using the method of Laplace transforms. y'"' + 7y"…

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Q: 4. If f ) و show that fg & LC₂.

A: Please find the answerin next step

Q: Use the method of variation of parameters to solve the initial value problem x'=Ax+ f(t), x(a)=x₂…

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Q: 195,000-40,000 is 155,000

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Q: Iff: X→ Y is a function and F is a nonempty family of subsets of y, then o(ƒ˜¹ (F¹)) =ƒ˜¹ (0 (F)).

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Q: Show that So e-ax J₁ (bx) dx= 1 √(a³ + b³)³ (a > 0)

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Q: For all a > 0 and b> 1, the inequalities In (n) ≤ nº, n < b are true for n sufficiently large (this…

A: Please see the attachment

Q: By using Value of fixed point approach solve the A = √2 + √2 + √2+...

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: 3. PDE r + a²t = 0, has the solution :

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Q: 4. Sydney is saving for a down payment on a new home. Each month she deposits $150 into an account…

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Q: Solve each problem by using composite functions. Be sure to show all work.  A manufacturer sells a…

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Q: Question 2 Given the data as in Table 2. x y 2 2.757 Table 2 3 7 3.279 6.009 9 9.751 12 12.906 15…

A: Given is a data in a table 2 as x 2 3 7 9 12 15 y 2.757 3.279 6.009 9.751 12.906 15.988   To…

Q: Estimate the following definite integrals using the Trapezoidal rule and Simpson's rule. Estimate…

A: 2 Given integral is ∫−11x2+1dx. We have to estimate the given integral by using Trapezoidal rule and…

Q: The measurement of the radius of a circle is 16 inches with a possible error of 0.25 inches. The…

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Q: г 3х +4 хих н d x

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Q: Express the periodic loading shown using Fourier's series expansion. F(t) F(t)= (1) Oct 25 +++ 0…

A: Given Ft=F0sin3πTnt0&lt;t&lt;2Tn302Tn3&lt;t&lt;Tn

Q: Consider the model dP dt where P(t) represents the size of the population at time t. = 5P + 10P²,…

A: In logistic model as competition increases ( i.e. population growing ) resources become increasingly…

Q: Find the sum of 73 ㅈ5 11.3 3.5 ㅗ ㅈ - + ㅈㄱ 15.7 + n-1_2n+1 ㅈ (1)h 12n-1 (2n+1)

A: We can solve as follows

Q: 2. Find all the 6th roots of 32-32√3i.

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Q: Determine the convergence of the following sequences. {sech n} a.

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