Theorem 5.1-1: If X - U(a, b) , then (b – a)? elb - ela M(t) = 3 t(b – a) a+ b and t + 0, %3D 2 12 1, t = 0.

Q: Let r(t): = 1 t-1' +-1/2). Find the domain of r(t). et+1, t-1,

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Q: A 3. Find (f g)(x) if f(x) = x2+x +1 and g(x) = x2 - x- 1. %3D %3D O (f 9)(x) = a4+ 2a + 3x? +2x +1…

A: We can find (f·g)(x) as below

Q: r(t) =(sin 3t, cos 31, V7t), 1. Let a) Find T(t) and N(t)

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Q: Question 4 Consider a consumer who consumes three goods, 1, x2 and r3. The consumer's consumption of…

A: Given: x1(p, s, w, y)=p2yw-sy=0             x2(p, s, w, y)=3yw-1sw=2             x3(p, s, w,…

Q: Consider T(r1,12, Ia) = (371 – 212 + 4ra, I1 + 273, 12). Find T!. %3D

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Q: (d) Calculate the coefficients (B's) by estimating separately the following models (Use the formulas…

A: The coefficients of β's can be estimated by using the method of least squares.

Q: 1.4 Which of the following equations are linear? (iii) x = -7y + 3z (i) x + 5xy – 2z = 1 1 (v) VTx +…

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Q: QUESTION 1 Let f(x) =x- 2 +8. Compute f-1(5): %3D

A: Given that         f(x) = (1/2)√(x-2) + 8  Here we have to compute f-1(5).

Q: (c) Determine the values of a and b if T(x,y,z) = (2x+y+z,a+3y,b+4z) is not self- adjoint.

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Q: Use Cramer's rule to solve for y (y only) in x+y=z=6 3x - 2y+z=-5 x + 3y - 2z = 14

A: The given system of linear equations, x+y-z=63x-2y+z=-5x+3y-2z=14 We have to find the value of y…

Q: Given P₂ = { a+at+at² | ª, ª, a are reals } B= {1-1², t+t², 2-t-t²} and E= {1, t, 1²} [1] Show that…

A: Given:  B=1-t2, t+t2, 2-t-t2 E=1,t,t2 To find: The E coordinates of qt where qB=-123 using change -…

Q: (H.W) 1) Draw the graph for the function Y = x and then find (Df) &(R). 2) Draw the graph for the…

A: we have to draw the graph and find the domain and range of the given function.  Domain-graph where…

Q: Define briefly u(t) and 8(t)

A: u(t): u(t) represents the unit step function, which is defined as u(t) = 0 for t < 0 and u(t) = 1…

Q: If f(z) = z² − (z)² + zz, calculate the following: a) u(x, y) and v (x, y) b) u(-10,-5) and…

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Q: Gauss Theorem: 2 Fi (a,b;c; 1) = r(e)r(c-b-a) r(c-a)r (c-b)

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Q: find the values of c that satisfy Rolle's Theorem

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Q: Example 23: Show that, if Y (t) = X (t + a) – X (t – a), then, (i) Ryy (t) = 2 Rxx (t) – Rxx (T +…

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Q: (c) cos(t+ T/4)8(t) (d) (t+1)8(t)dt + 1)8(t)dt (e) (t – 5)dt +1

A: (c) Concept Used:-δ(t)={0if t≠0∞t=0Consider cost+π4δ(t)=cost+π4.0t≠0∞t=0Hence cost+π4δ(t)=0t≠0∞t=0

Q: +3. . Find the linearization of _9). Can you tell anything about the error? at (3,2). Evaluate at…

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Q: The functions f1 (z), f2 (z) and f3 (z) defined in the following equations (being EC) are given. i.…

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Q: (а) Р(0, 1), t %3 /2 t = (b) Р 2 (с) Р( — 1, 0), t%3D (d) Р 2 2 (е) Р(0, — 1), t 3 () P(- (f) Р 2 /2…

A: a. Given point, P(0,1)

Q: 9. In this exercise, T: R2 R2 is a function. For each of the following parts, state why T is not…

A: Given function is T:R22 is function we have to prove that why T is not linear in upcoming parts.

Q: For the given signal, Sketch: a) x(t) d b) a x(t) dt c) x(a) da ∞ x(t) = 0 -t -1 t-3 0 t 3

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Q: Evaluate (t? + 6) (t² + 9) dt using the Fundamental Theorem of Calculus, Part 2. | (t? + 6) (t² + 9)…

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Q: Let Te B(H) be an invertible operator. Show that a(T-) = 0(T)-.

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Q: Calculate f (3xy + 4e²) d.S, where S is the triangle with vertices (0, 0, 3), (1, 0, 2), and (0, 4,…

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Q: 23)a)givenx(t) and y(t) as below (3) y(t) X(t 2 4 2 Oplot x 1-0.5t) i)plot y(2t+1) iii) find x((1–…

A: Given that:   To plot x1−0.5t and y2t+1 Also to find ∫04x1−0.5ty2t+1δt−1dt

Q: 1) Find whether the signals are memoryless or memory? a) y(t) = 5x2(t+2) b) w(t) = (t-9)x(t)

A: a) Given signal is: yt=5x2t+2 Substitute: t=1. y1=5x21+2y1=5x23 So, the output at t=1 depends upon…

Q: Question 7 Sslanta 122-9) Identify the correct u A (2y²+3)2 B ® (2+3) © (2y²+ 3) D 4y4+12y²+9 E None

A: Identity the u=2y2 +3

Q: X; - X-1 = (H + y;) – (Hi-1 + yt–1) (2.27) = 6 + W; + Yt - Yt-1. It is easy to show z; = yt – Yt-1…

A: A weakly stationary vector  (X1,...,Xn) and time shifted vector (X1+h,...,Xn+h) has same mean and…