Given that: dy lim da Ax÷0 Ax(√x√√x+^x) (√x+√x+^x) - dy dx Determine 1 r=1 - Ax A (To one decimal place)

Q: Find the power series representation for the function and determine the radius of convergence.…

A: We have to find the Power series representation of f(x) = x2ln(1 - x) We know ln1+x=∑n=0∞-1nxn+1n+1

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A: The main objective is write two non zero vectors in ℝ5. Find the given values.

Q: +|m₁nEN ² mine 3. Let S = { (-1) ²² [ +1 +224131 Find all cluster points of S

A: S=-1m+n21m+2n+12n+3 m,n∈ℕ

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Q: dy 6. The differential equation (1+x²) - 2xy = x + x³ has the general solution dx y=e³(x+¹)+C 4 (A)…

A: The given problem is to find the general solution for the given differential equation.

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A: Given, r¯(u,v) = ucosv,usinv,v, 0≤u≤30≤v≤3π   We have to find the surface area of the helicoid.

Q: = 2f X Discuss the monotonicity of g(x), where g(x) 2 + f(6-x²) Vxe R. It is given that f"(x) > 0Vxe…

A: g(x) = 2f(x2/2) + f(6 - x2)  => g'(x) = 2xf'(x2/2) - 2xf'(6 - x2)                = 2x[f'(x2/2) -…

Q: 11:2 +¸µ¹¹:¹² + z ¹¹12 Prove that x12 denote differentiation w.r.t.s. = 1 p² 0² + 1+p²². 04 11 1 R²…

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Q: Calculate the integral using cylindrical coordinates: ∭U√x2+y2dxdydz. The region U is bounded by the…

A: Evaluation of the triple integrals using cylindrical coordinates

Q: Evaluate the integral (curl F). n dA directly for = [e²z, e² sin y, e² cos y], S: z = y²(0 ≤ x ≤ 4,0…

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Q: Consider the matrix equation Ax = b: [1-2 1 1 -4 3 2 2 After Gaussian elimination is complete, which…

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Q: Find the mass of a thin funnel in the shape of a cone z =√x² + y2, 1 ≤ z ≤ 3, if its density…

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Q: Please

A: Here we find solution by Gauss Jorden Method, Inverse of matrix method and varify it.

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A: Given:y= fx, a≤x≤b To find:  (a) Parametrization ru, v of S. To show  (b) The surface area of the…

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A: We use properties of ring to prove our claim.

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Q: Let y = 3 1 [] [-] and u = 4 -7 Write y as the sum of two orthogonal vectors, one in Span {u} and…

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Q: Consider the following matrix: -18 0 5 0 20 -30 -3 10 0 40 0-30 0 A = 0 0 0 0-30 -15 0 5 0 17 a)…

A: A=-1805020-30-31004000-300000-30-1505017

Q: please show all work 5.    Consider vectors u = [3,−3,2], v = [2,3,−1] and w = [−2,−4,2] (a)…

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Q: Consider the primal LP problem given below: The optimal tableau is given by: Basic Variables 1. 2 81…

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Q: Use Fourier series to evaluate the following infinite sums 1 1 1 4₁=1++: + + ...8 8 27 64 1 1 1 1₂ =…

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Q: Questions 1-10 are concerned with the equation: +6+9y=9x 1. What is the order of the equation? a. 0…

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Q: 2. (a) Let S= A 0 I B A, B & GL (R), B = B, A = (B n ¸ Check whether or not S SP2n(R). Also give an…

A: Here , I use latex to write the answer.

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Q: True or false: Answer "True" or "False", and justify your answer.   1. Is the equilibrium solution…

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Q: Given, f(x)=x2-4x, [−4,8]. Find R3,L3,and M3 and give accompanying accurate sketches

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Q: · Let S : RCUN) = < u² Losv, u²³-4, 4²-sinv), (u₁v) & [13] x [2₁4] Evamate : do (y+4)³2 SS S

A: Note: For r→(u,v)=&lt;x(u,v), y(u,v), z(u,v)&gt; , take dσ=||ru→×rv|→|dA

Q: 2.    Consider a linear system below: 2x − y + z = 2 x + 2y − z = 5 3x + y + 2z = 5 (a)    For the…

A: Given the linear system of equations is,…

Q: please provide the correct answer

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