Suppose that you have three vectors: f1 (x) = 1, f2 (x) = x – 1, and f3 (x) = } (x² – 4x + 2), that make up an orthonormal basis spanning the real vector space of quadratic functions with the inner product: (f: | f;) = L° fi (x) f; (x) e¯²dx. Suppose we have a derivative operator D = . What is (fi |D| f3) =? -1 2 3/4

Q: Find the limits of the following vector functions. 2t³-t² tan (2t)\ 21² (i) (ii) lim In 1-0 5t lim…

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Q: Let 3 = (X'X)-¹X'Y as shown in class. Let y = w'ß, where w is a column vector. Show that Var(y) =…

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Q: Find the number of zeros of f(z) = z' + iz² – z + 2i in the upper half-plane.

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Q: 1 f(z)=- (r+,2) +4)

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Q: Suppose f(x, y, z) = xyz + 2xy + 2² · Compute the following values -(2,8₁16) - (-2,-8, 16) (1,-1,0)…

A: We have to find functional value.

Q: Find the limits of the following vector functions. -2) 21³-t² tan (21) 21²" (i) (ii) lim In 1-0 5t…

A: Since you have posted multiple questions, we are supposed to answer only first  question. If you…

Q: Exercise 6: Suppose f and g are functions such that: -3 f = 1, i=7, f = 5, -3 Г» g = 6, g = 3, :-4.…

A: Suppose f and g are functions such that

Q: (1)-(9-1²₁.sin(√²²-9)). Find the domain of the vector function, r(t):

A: To find the domain of the given vector function

Q: Determine which of the following pairs of functions are linearly independent. NO_ANSWER f(x) =e5 "…

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Q: Find the domain of the vector function T (ty= Vt + 7 Domain: {t <t< }

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Q: Let R be a differentiable vector-valued function such that R'(t) = (3t2, 2tvt2 + 1, 2t + 3) and R(1)…

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Q: R(t) = = {{In(3 In(3 – t), (0, -1, 4), 4t-8 4-t2⁹ 8), 3t² – 8 t#2 t = 2.

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Q: 3 - Find the Derivatives of the following Vectors, Where F(t)* = 2secti – 3j* + csctk and G(t)* =…

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Q: The answer I provided for (x-5)^2 is said to be wrong. Please help me rectify the problem. Also…

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Q: Consider the following bijections on R: f (x) = - g(x) = x – 7 Then (f o g)¯'(x) =

A: Given, fx=-x,gx=x-7 Find the value of f∘g-1x.

Q: Show that fi (x) = cos x , f2(x) = cos 2x are orthogonal on [-7,71]. %3D

A: This is a application of integration problem

Q: Let f(x, y, z) = x2 (e)^y/z. Compute f(-1, 0, 1), f(1, 3, 3), andf(5, -2, 2).

A: Let fx,y,z=x2eyz 1. we have to compute f(-1,0,1) as, fx,y,z=x2eyzHere x=-1, y=0,z=1f-1,0,1=-12e01=1…

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.