Given ƒ"(x) = 7x +5 and ƒ'(0) = −2 and ƒ(0) = 1. Find f'(x) and find ƒ(4) =

Q: (4) If p(x) = ao + a₁ + a₂(1 + x²), calculate L" (p(x)).

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Q: Why is the set {91 +124t² - 61t³, 66 − 58t +93t², 22 + 248t — 87t² } not a basis for P3(R)? Select…

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Q: Suppose A is the symmetric matrix below: A has the eigenvalues and unit vectors: The spectral…

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Q: = ²√x = by identifying the domain and any symmetries, finding the derivatives y' and y", finding the…

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Q: Find a particular solution of the indicated linear system that satisfies the initial conditions ×₁…

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Q: 2. Assume that Σak <∞, prove that are converges uniformly on [-1,1].

A: We are given that ∑|ak|&lt;∞ , which means the series of absolute values of the coefficients…

Q: (ii) Calculate the value of ||q|| (with respect to the given inner product).

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Q: Consider the two bases B = {b₁,b2} and C = {₁, 2} for R² where 3 5 = = - [B]-4-[13] 4-[8]), 4-[8] =…

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Q: Using the definition, determine the Laplace transform of the function. 3, 0≤t≤5 f(t)= t, 5<t≤00

A: Here the value of t ranges from 0 to infinity. We know f(t) is given we need to find F(s).

Q: c. B: = [3 5] 8 [4 5] {[][114])} 2 3 X

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Q: Let H be the subspace of R³ spanned by the vectors Suppose y EH with [y] = H . Compute y. 3 4 0-0 -4…

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Q: The graph below is of a function g(x). -3 -2 Use the graph to estimate Enter a number, 7 -1 (a) a…

A: The graph below is of a function .By using the graph to estimate , by using six sub-intervals of…

Q: A house sells for $165,000 and a 15% down payment is made. A mortgage was secured at 4.7% for 30…

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Q: Exercise 10.2.2 Finish the proof of Proposition 10.11, i.e., prove that if T:VW is a linear…

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Q: 4. y"+y = √2 sin √√2 t, y(0) = 10, y'(0) = 0 Ans. y = 10 cost + 2 sint-√√2 sin √√2t

A: The given problem is to find the solution for the given non homogeneous linear differential…

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Q: 1. Consider the sets D = { // : n € J}, E = DU{0}. (a) Really quick: complete the definitions - (a)…

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Q: Motors Inc. manufactured 306 cars with automatic transmissions, 237 with power steering, and 62 with…

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Q: Find a general solution to the given differential equation using undetermined coefficients. y" + y =…

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Q: 2. Determine the Laplace transform of the given function. a) f(t) = e³¹ +4 c) f(t) = est sin(3t) e)…

A: Let Then Result:

Q: Express the following integral as a double integral in polar coordinates 1 Suvaldy x² + y² dy dr

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Q: Let a vector field given by V=V x W where W is an arbitrary vector field. O is always potential O V…

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Q: Using the Fourier sine/cosine integral to solve the given integral equation for the function f(x)…

A: Using the Fourier sine/cosine integral We have to solve the given integral equation for the function…

Q: 3. Let X and Y have the joint distribution as indicated in the following table: X=0 X=1 |Y=0 1/3 0…

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Q: Let a E R. Let f be a function defined on R. Is each of the following claims true or false? Prove…

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Q: y" − 2y' + 5y = 0, y(0) = 0, y'(0) = 2. -

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Q: A 1 kg mass is attached to a spring with a spring constant k = 9N/m. A periodic force F(t) = cos(wt)…

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Q: Problem 5. Prove that the space X is Hausdorff if and only if the set ▲ = {(x,x) : x ¤ X} is closed…

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Q: A matrix A and an echelon form of A are shown below. Find a basis for Col A and a basis for Nul A. A…

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Q: Calculate the adjugate Adj(A) of the matrix A= 2 Select one: O 2 1 2 301 4 2 1 3 1 2 1 2 4 4 3 1…

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Q: Let f f(x)dx = 8 and f(f(x))²dx = 9. Find the following integrals: So cf(z)dz = f(f(x))²dx − (f…

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Q: A linear second-order non-homogeneous equation models this scenario: People falling at a height of…

A: The objective of the question is to represent the given scenario as an initial value problem in…

Q: Let A =[1 -1]            [2 0] and --->x =[ i]                  [1 + i] . SHOW that Re (A--->x )…

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Q: Write the vector v = :8 + 3t+t² as a coordinate vector with respect to the basis B. NOTE: Each set B…

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Q: Q(t) = Find an antiderivative of q(t) = (t + 1)³

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Q: Problem 2. Let dX/dt = AX. Find et and use it to write down the solution to the system. (²2) 1 a) A…

A: Since you have posted a multiple question according to guidelines I will solve first(a) question for…

Q: Hello, hoe about #2

A: The given function is in branch We can find Laplace transform by defination .

Q: Find a unit vector in the direction of the given vector. 80 - 150 A unit vector in the direction of…

A: The given problem is to find the unit vector in the direction of given vector.Given vector

Q: Let A = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4} and define a relation R on A as follows: For all x, y E…

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Q: Consider the sequence Xn = + We wish to prove that. Xn → 0. Given e > 0, we must find NEN such that…

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Q: and Assume |A| = 16, |B|=18, |C| = 28. If , how much is given |AnB| = 7 |AnC| = 11 |BC| = 8 AUBUC…

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Q: 2. In a vector space V with inner product (,), the vectors u and v are orthogonal and ||u|| = 3 and…

A: Given thatIn a vector space V with inner product , the vectors u and v are orthogonal and We have to…

Q: 21. Let f(x) = 2x, x = [0, 1]. Take P = {0, 1, 1, 1, 1, 1} and set x₁=1, x₂ = 16, x3 = 3, x4={, x3 =…

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Q: 8. Si 0. si xo < 0. si xo = 0

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Q: Exercise 10.4.4 Let T: R² R² be a linear transformation defined by T ([%])=[a+b]. Consider the two…

A: The given linear transformation .The two bases  and .The aim is to find the matrix  of .

Q: F(s) = s+1 2 S² - 2s+2

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Q: Assume that f is continuous everywhere. Show that for any non-empty subset UCR, if U is ajar, then…

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