Find of the operstor a norm A(x) = S (2.+st)x(t)dt %3D A: C [o,1] →L [o,I] O a. 2 O b. 7/12 O c. 11/12 O d. 1/2 O e. 1

Q: Consider the function f(x, X2, X3, X4) = x+3XX4+2x2 8xxX4 +3x+7xa? O a. Fis positive definite Ob.…

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Q: Consider F and C below. F(x, y, z) = yzexzi + exzj + xyexz k, - C: r(t) = (t² + 1)i + (t² − 1)j +…

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Q: Show that the function a Y1 (x, y) = [21 2] в с Y2 is an inner product on R? if and only if b2 – ac…

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Q: (a) Let be a a- Algebra on X. Assume that , lz: - (0, oo) are two measures on X. Is + kuz a measure…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: S. (1+x²)² da is

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Q: O {1, z+ 3, 2a, sinz In 2,1

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: Compute [ f(x,y) dA, where f(x,y) = y²√ and D is the set of (x, y) such that x>0, y> x², and y<10-…

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Q: Let f(æ1, x2, X3)=(x1³ + x2, x1? + x3). Find df(1,2,3) (-3, –2, –1)

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Q: Find a norm of the operator A(x) = o (s4 + s? )x(t)dt in space C[0, 1]. a. 4 Ob. O c. 2 4 O d. 15 1…

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Q: et r be a three-dimensional real vector-valued function such that r′′ exists. Show that d/dt [r(t)…

A: Given: r is a real vector-valued function in three dimensions, and r'' exists. Our aim is to show…

Q: 2) Explain the definition of linear independence/dependence of n functions fi(x), f2(x),..., fn (x)…

A: The given functions are f1x,f2x,...,fnx and also the sine functions are sinx, six2x, sin3x. To…

Q: ( E)i+(G + log(vF –1 – 1) + (5ť² +1 – log t)k |3 – V7 – t2| t2 – t – 1 T(t) =

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Q: 4. Consider the vector-valued function R(t) = a. Find the domain of R b. Show that R is continuous…

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Q: 2. Show that e*, sin x, cos x are linearly independent using Wronskian Method.

A: As per the policy of bartleby the provisions is to solve only one question at a time  I am solving…

Q: Let r(t) = ⟨t, t, t⟩. Compute r'(t) and interpret the result.

A: rt=t, t, t

Q: Given u(x)= x +3 and v(x)= 9x – 4, find u v. O 9x² – 12 - O 9x² + 27x – 4 O 9x+ 23 x - 12 O 9x + 23…

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Q: Find the value of a,b ∈ R ,so that the following sets of functions are linearly independent for all…

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Q: Consider the vector-valued function F(t) = exists. 21-6 In(-2) ²³-2t, 2-4t+3/ Find lim F(t), if it…

A: Here we have to find limit of given vector valued function.

Q: [D²,2²] = 2(2&D + î) 2(2£D + î) Prove that

A: The function f(x) is a rule that associates or fixes a number to the particular point x. If y=f(x),…

Q: Consider the function vec : Cmxn → Cmn such that for any A E Cmxn A*1 vec (A) = = A*2 : A*n Prove…

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Q: ion 7(t) = e' i +Gj+ In(t² – 4) k

A: We have to solve given problem:

Q: The graph below represent the domain of the function O f(r, y) In(1 -+y) Of(r, y, z) = VI+y-1 Of (r,…

A: The given graph represents x+y&gt;1. The domain of ln(1-x+y) is 1-x+y&gt;0⇒-x+y&gt;-1⇒x-y&lt;1. So…

Q: Consider F and C below. F(x, y, z) = yzex² i + eײj + xye×z k, C: r(t) = (t² + 5)i + (t². (a) Find a…

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Q: Recall that for D a squarefree integer, the norm function N on Q[VD] is defined by N(a + bVD) = (a +…

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Q: Find a norm of the function f(t) =t – 2t in space L10, 1] 1 a. 6 С. е. d. ai

A: We use the definition of norm in L1[0,1] to answer the given question.

Q: Consider F and C below. F(x, y, z) = yzexi + e*²j+xyek, C: r(t) = (t² + 1)i + (t² − 2)j + (t² − 3t)…

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Q: I. Consider the vector-valued function In(2t + 1) Ŕ(t) = ²₁+ î+ t 1. Determine the domain of R. 2.…

A: This is a problem of Vector Calculus.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.