1. Find the local linear approximation of f(x)=√xe¹5-3√ at o = 25. Use this to estimate √25.1e15-3√/25.1

Q: Ut = Uxx, 0 0, u(0, t) = 0, u(1, t) = 0, t > 0, u(x, 0) = x(1-x), 0<x< 1

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Q: Find the general solution of y" + 2y' + 5y = e²t. Put the final answer in the box provided.

A: The given differential equation y''+2y'+5y=e2t. We have to find the general solution to the…

Q: For Vector fields with va (X.X)= x VY (X. y) = y X U* (x.y) =~Y U (x.x) = x Compute the Lie…

A: Given: Vector Feilds with Vxx.y=x   Vyx.y=yUxx.y=-y  Uyx.y=x We need to compute the Line derivative…

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A: Dienes' blocks, also known as base-10 blocks or multi base arithmetic blocks, are a manipulative…

Q: 29. Let T be the linear transformation whose standard matrix is A = one-to-one and whether it maps…

A: T is a linear transformation and the standard matrix for T is:A=1-23-13-42-5-2 To Do:We have to…

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Q: The lth Legendre polynomial is given by P(x) These satisfy Legendre's equation ((1 − x²) P{(x))' +…

A: Integration by parts: ∫udv=uv-∫vdu

Q: y" - 2y' +4y=0; y(0) = 2, y'(0) = 0

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Q: s]: Two vectors are à = 2x + 4ỹ − 32 and B = −7ŷ – 2. Find: Question #1 (i) The magnitude of vectors…

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Q: 3. Compute the eigenvalues and eigenvectors for the matrices 103] 0 1 0 301 and [1 -√√2 3] 0 0 3 2 1…

A: The given matrices are  103010301 and 1-230-203-21.

Q: Use the Divergency Theorem to evaluate F. Nds and find the outward flux of F through the surface of…

A: F(x,y)=(xy2+cosz)i+(x2y+sinz)j+ezkS:z=12x2+y2,z=2. By using Divergence theorem to evaluate the…

Q: 2x+3 5 c) Restrict the domain of the function f(x) b) Given f(x)= = and g(x) = x - ² show that f(x)…

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Q: Solve xy' + 4y = y; y(1) = 2

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Q: 2. Evaluate 11 [² (²+ €²) du)} (s 3. Solve the D.E. using Laplace Transfor y + 5y +6y=0 y(0)=0 47001

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Q: Use the Chain Rule to evaluate the partial derivative at the point (r, 0) = (2√2, 4), where g(x, y)…

A: The given functions gx, y=1x+y2, x=8r cosθ, y=11r sinθ. We have to find the value of ∂g∂θ|r, θ at…

Q: Translate this sentence into an equation. 105 is the product of Goran's score and 7. Use the…

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Q: Let 0 and vs= Use the Gram-Schmidt procedure to produce an orthogonal set with the same span. (Hint:…

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Q: Find 9 dx

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Q: Solve the following differential equation by using Laplace transform y"(t) + 2y'(t) + y(t) = et ;…

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Q: so the answer is x^3 =8 because x=2 there 2^3=8

A: One example of an equation that satisfies all the given conditions is:   e^x - e^3 = 0   In this…

Q: Exercise 6.9 In the Euclidean space: a) Find a plane passing through the points P = (1, 1, 1) and Q…

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Q: Is every binary representation, i.e. sequence of rational numbers of the form: (91, 92, 93, ...) =…

A: A Cauchy sequence is a sequence such that ∀∈&gt;0,∃ k∈ℕ  s.t.  |xm-xl|&lt;∈∀m,l≥k i.e. as the…

Q: Use projection matrices to find the matrix exponential and particular solution of the given linear…

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Q: differential equations please solve questionnnnnnn 10

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Q: X Let F(x) = [² t³e-0¹ Find the MacLaurin polynomial of degree 12 for F(x). T12 = dt. 0.83 1.000.…

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Q: Solve the following IVP using Laplace transform y" + 3y' + 2y = 6et, y(0) = 0, y'(0) = 1

A: Laplace transform of derivatives:1.L[f11(t)]=s2F(s)-sf(0)-f1(0)2.L[f1(t)]=sF(s)-f(0)Laplace…

Q: Find the general solution to y - y"" = x+e*; y(0) = 0, y'(0)=0, y"(0) = 0, y""(0) = 0

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Q: B- Find Inverse Laplace transform of the following functions F(s)= 2s-7 (s+ 6)(s² + 4) G(s) = s(s² +…

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Q: e (1) Given the following clauses: (PVW)^(PVQVT)^(-S)^(PVQVS)^(-QVT)^(-T) ^ (W) Perform the smallest…

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Q: of a The Values at the following X 3 Approximate s f(x) dx function Values 0 0.25 0.5 0.76 4 8 f(x)…

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

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Q: 7. Let B be the unit ball. Evaluate dxdydz √2+x²+y²+z²* Show the work!

A: We have to find the value of ∫∫∫Bdxdydz2+x2+y2+z2, where B is an unit ball.

Q: (a) ( Consider the following proof with missing parts (indicated by bold, underlined digits 1. 2. 3.…

A: We need to complete the proof to show 23 is irrational.

Q: 5. Expand f(z)=2/((z+1)(z+3)) in a Laurent series valid for (a) 1<|z|<3, (b) 3<|z], (c) 0<|z+1|<2,…

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Q: Compute ||A||||A||₁, and ||A|| 1' ||A|| F || ||A||₁ = ||A|| 00 II A = 12 0 [ 6 -3 -4 5 1 -6 6 -3

A: A matrix A=0-4561-6-3-36 To Find: AF'  , A1' , A∞

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Q: Determine which of the triangular surfaces of the irregular tetrahedron are intersected by triangle…

A: Given is a tetrahedron and a triangular lamina. The two intersects and the triangular lamina…

Q: Hi Sir, sorry i was typo, it suppossed to :  σ = x2y please accept my apologize, my mistake

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Q: Solve 1-2 x + 5 2-x x+6 without the use of a graphing calculator. Show all work.

A: The given problem is to evaluate the given inequality. Given inequality, (1-x)/(x+5) ≥ (2-x)/(x+6).

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Q: "There exists a set crue or false? stify

A: False. The statement is false. The set Y cannot guarantee that every function from X →Y (the set of…

Q: A tank initially contains a solution of 5 pounds of salt in 40 gallons of water. Water with 3/5…

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Q: Proceed as in this example to find a solution of the given initial-value problem. 2x y" - 4y = e²x,…

A: y''-4y=e2x , y0=1 , y'0=-6 To Find: Solution of the above problem.

Q: If the birth rate of a population is b(t) = 2300e0.021t people per year and the death rate is d(t)=…

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Q: (b) Evaluate whether the following argument is correct; if not, then specify which lines are incor-…

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A: Debt=$15,000  Interest rate=6.8%

Q: differential equations please solve questionnnnnnn 4

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Q: 2 Find Valure for the solid whose height Zoxy) = x-xy and bass bounded by y=x, y=3x-x²

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