y' - ycosx = cos x

Q: Sketch the graph of the function. (3x + 3, X ≤ -1 k(x) = 3x²-2, -1 1 y

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Q: Use Lagrange multipliers to find the maximum and minimum values of the function f(x,y,z) = x² + y²…

A: Here we use the Lagrange multiplier to find extrema of function by finding the partial derivatives…

Q: A map f:x-y is said to be an open map if for every open set U of X, the set f(u) is open in Y. Show…

A: Given, a map f: X→Y is said to be an open map if for every open set U of X, the set f(U) is open in…

Q: An electrical circuit consist of a series connected resistor (100 ohms) and a capacitor C = 0.01 µF.…

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Q: f is represented by the matrix: A = (0 2) (7 8) Show that f is invertible and find the…

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Q: Graph the derivative of the function f(x) if the graph of f(x) is

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Q: Compute the derivative of the vector-valued function: r(t) = x²+4 In+i+ sin ² tj + (t² + 1)²k x-5

A: We have to compute the derivative of the given vector-valued function rt

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: 1. Determine the convergence of the following sequences. 1 b. n²n!

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Q: A Markov system with two states satisfies the following rule. If you are in state 1 then of the time…

A: Consider the give system. We have to write the transition matrix for this system using the state…

Q: 3 16 If 7 is an 7(2)= [ Rational irrational About Then entir what 1

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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: How many solutions are there between planes P₁: 2xy + 2z = 2 and P₂: -x + 2y + z = 1? If there…

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Q: Q4. Consider the topological space (X,T), where X = {a, b, c, d) and T = {o, X, {a}, {b}, {c},…

A: Given: Q4. a)  X, T is a topological space, where X=a, b, c, d and T=∅, X, a, b, c, {a, b}, {a, c},…

Q: Solve the linear programming Maximize: P = x + 2y-z Verify your Solution Start: X2424 11252 -1 -2…

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Q: Prove that Let p be a prime. Then (p−1)! ≡ −1 (p)

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Q: If y, and y₂ are linearly independent solutions of ty" + 4y + tey = 0 and if W(y₁.₂)(1) = 4, find…

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Q: 5. x=4-s+t Find a vector perpendicular to the plane = y = 1+ s-t (z=1+s+t b) [5, 5, 0] a) [1, -3,…

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Q: a.V odv

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Q: Let (G1, ) and (G2, *) be two groups and : G1 G2 be an isomorphism. Then * O G2 might be abelian…

A: Let G1 , ∘  and G2 , * be two groups. Consider , ϕ : G1 → G2  be an isomorphism. We know that , ϕ is…

Q: The number of air safety inspectors for selected years is shown in the table. Year 1996 1997 1996…

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Q: Using the Euclidian algorithm find the inverse of the following 1) 57 modulo 113 2)13 modulo 20…

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Q: Question 2 Determine the Riemann integral *¹2 Jo partitions given by P₁ = Qn = 1 2 4n' 4n 4' 4n 12…

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Q: A point P(3,0,5) lies on a plane that can be defined by the scalar equation Ax+By+Cz+ D = 0. A…

A: the scalar equation of a plane with normal  vector n=(A,B,C) is  AX+BY+CZ+D=0

Q: (b) Obtain 3 non zero terms of the Maclaurins series for sin²x. Hence, evaluate sin² x 0.5 1.0.5 5…

A: The given problem is to evaluate the given definite integral using Maclaurin series of sin2x upto 3…

Q: Find an equation of the line in parametric form that passes through the vertex of the paraboloid…

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Q: A ball is launched straight up in the air from a height of 5 feet. Its velocity​ (feet/second) t…

A: The velocity is the rate of change of the distance with respect to the time. Hence, it can be…

Q: Show that * Ső› X yn+¹ J₁ (xy) dy=Jn+1 (x)

A: Using the recurrence relation of bessel function

Q: 2. The differential equation (x² +1)y"+ay": = 0 and the following data are assumed; X y 0 0…

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Q: For all a > 0 and b> 1, the inequalities In (n) ≤n", n < b are true for n sufficiently large (this…

A: We write an inequality comparing (ln(n))8 and n.

Q: How long will it take money to quadruple with continuous compounding at 12% interest? 15,019 72 Ob…

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Q: we the following linear diffe D² - 2D + 1) y = x² e³x,

A: *By Bartleby policy I have to solve only first one as these are all unrelated &amp; lengthy…

Q: Q4) Using Numerical Integration to estimate area between curve (y=2-x) and line (y=-x), with n=3

A: Introduction: The formula of the trapezoidal rule for the numerical integration is given by,…

Q: Find the indicated limit. Note that l'Hôpital's rule does not apply to every problem, and some…

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Q: a) A flexible string of length is tightly stretched between x = 0, x = π, on x-axis, its ends being…

A: The given problem is to solve the given partial differential equation with given initial conditions…

Q: 13. If a and are the zeros of p(x)= 3x² - 6x +4,find the value of (i) a² + B² (ii) a/ Bß + B/a (iii)…

A: The given problem is to find the value of the given identities from the given polynomial function…

Q: The number of air safety inspectors for selected years is shown in the table. Year 1996 1997 1998…

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Q: explain the purpose of a proof by ε, δ definition of a limit.

A: Here I give the geometrical view of definition.

Q: You want to estimate how many fish there are in a small pond. Let's suppose that you first capture…

A: Here given n1=600 fish, n2=30 fish, and k=8  Consider the estimated number of fish in the pond is N.…

Q: prove that 12 div A; = √√√x² {√8 8¹k Ax} = dxr div A¹, where A; and Ai are the covariant and…

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Q: A population has the following characteristics. (a) A total of 75% of the population survives the…

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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: function f(x) = x as OLX 22 Expand the cosine series in sine series in 0 2x 42.

A: Here given that f(x)=x. We expand f(x) as cosine and sine series in 0&lt;x&lt;2.

Q: 3 1 1 2 accountants can do 4 tax returns in returns can 3 accountants do in 3 hours? Find the…

A: Given that 112 accountants files 134=74 tax returns in 112=32 Then 3 accountants will file…

Q: 1. Determine the convergence of the following sequences. C. 3n {(²1+5) ³7}

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Q: Apply the method of undetermined coefficients to find a particular solution to the following system.…

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Q: Plot the following planes and the normal vectors of each plane. 3x - 6y +9z = 9 x - 2y + 3z = -4 2x…

A: We will use inter relation between planes to find there relation . As solution of two graphs gives…

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: г 3х +4 хих н d x

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Q: By using polynomial division first, evaluate the integral of: ʃ (e2x + 1) dx / (ex + 1)

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