6. Show that if f : X Y and g : Y → Z are both onto then fg : Z -→ Z is onto. (Note this is function composition NOT multiplication)

Q: Write f(x) as a power series and give the interval of convergence f(x)=6/(1+7x^4)

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Q: 5. J_√x dx (4 + x)'

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A: This is a problem of topology.

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Q: 2. Letr =√x² + y² + z². (a) For n ≥ 1 and r> 0, express V(r-n) in terms of r and the radial vector…

A: Given  solution(a): Radial vector field  solution(b):

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Q: operation

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Q: B. Find the area of the region bounded by the following: 17. r=3sin 40

A: Here we can use the formula for the area of polar curve which is given as follows A=∫∫A r dr dθ

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Q: f(2) that maps: Find an analytic function w = 41. The infinite strip 0 0.

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Q: Match the vector field with its graph. F(x, y) = xi + 3yj KE 、 ||十

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Q: Question: Which of the following statements are true? A = {1,2,3,4}, B = {1,2,{3,4}}, C =…

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Q: e Stokes' Theorem to evaluate o F dr. F(x, y, z) = z²i + 26xj – y°k ere C is the circle x? + y = 1…

A: Line integral of the vector point function

Q: 6) Find the measure of all 7 angles given that one of the angles is 115. Angle 1- Angle 5= Angle…

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Q: 11. Which system of linear equations has the solution (2, 3)? A. 2x - 5y = 9 x-y = 4 C. 9x - 8y = 19…

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Q: 4. The removal rate y measures the fraction of individuals in the infectious class that stops being…

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Q: b. » [*[*(x²y + xy²³)dydx

A: Solution :-

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A: We can solve this by solving the eigenvectors

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Q: (sin5 (x)) dx

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Q: Let C1 be the circle r = 3 cos 0 and C2 the cardioid r=1+ cos 0. (a) Find all point(s) of…

A: We will find point of intersection by equating both r .  If f is continuous and non negative on the…

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Q: Solve X'= %3D 1 2. 人 2. Given use %3D -2-2 Laplace TransForm OF A to Compute At.

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Q: What is the degree of a quadratic function?

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Q: A Power Set is the set of all subsets of A, and is denoted as (A). As an example, let A = {1, 2}.…

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Q: 5. Prove that for any vector x, we have (a) 1, <H<#H, (b)

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Q: 3 Evaluate F. dr along the curve C if F(x, y) = (x² + y²) ²(xi+yj), and C : r(t) = e' sin ti+ e' cos…

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Q: 1. 'Let X = {a,b,c,d,e} . Define ze P(x) by r={ø,X,{a},{c,d},{a,c,d},{b,c,d,e}}. ond nterore d) Give…

A: Let (X,τ) be a topological space and A be a subset of X, then the closure of A is denoted by cl(A)…

Q: 1. Find the saution YLEA oR Ele tntifial Value poobem y"-8y'+16y=8e*, yr0)=3,4'101=2,

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Q: Use the method of Laplace transforms to solve the given initial value problem, Here, x' and y'…

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Q: 3 1 (6) Consider the system z'= Ax + G, where A = and G(t) = (a) Decouple the system using the…

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Q: -. Use the binomial series to expand the function as a power series. State the radius of…

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Q: Given a line 2a + y = 2 in the two-dimensional plane, • If a given point (a, 3) satisfies 2a + B >…

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Q: 14. Solve the initial-value problem dY 4 -2 Y, Y(0) = Yo, dt 1 where the initial condition Yo is:…

A: We will use eigen values and eigen vectors to find general solution of given differential equation…

Q: 117.068 -23.332 S= - 23.332 40.668

A: Here highest eigenvalues value is the principal component.

Q: B. Find the area of the region bounded by the following: r=8sin² ¹0 16.

A: Here we can use the following formula for the area of the polar curve  A=∫∫A r drdθ

Q: 11r If F(r) and o is the surface (x – 4)? + y² + z² = 49 oriented outwards, what is the value of //…

A: We have to find the value of ∫∫σF·ndS where σ is the surface-oriented outwards.

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Q: For each of the following, factor the matrix A into a product QDQ" where Q is orthogonal and D is…

A: We have to factor the given matrix A into a product QDQT where Q is orthogonal and D is diagonal.

Q: Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. To save…

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Q: Expand (x + 4)(x – 5) and use this answer to write down the quadratic equation in the form ax2 + bx…

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