[cos w ((t1 -t2 Prove that Covariance (t, , t) = Auto correlation (t, , t2) = %3D %3D

Q: Determine f g a) f(t) = cos(t), g(t) = t b) f(t)=e¹, g(t) = e' sin(t)

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Q: Consider the function f(r) = (r – 1)e. a) When is f(r) = 0, when is f(x) > 0 and when is f(r) < 0?…

A: Given, f(x) = (x-1)ex

Q: of and for the functions: dx dy H.W: Find 1. f(x, y) = (xy-1)² 3. f(x, y) = (x²-1)(y + 2) 2. f(x, y)…

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Q: a.) If f(x)= sin(In(x* )), find f'(x). b.) If g(x) = 5x find g'(x). %3D .2 x +3

A: (a) Consider the provided function, fx=sinlnx3 Find the derivative of the provided function. Apply…

Q: Find the point D'4, symmetric of D4 with respect to the line F4B1. F4: (-2,1,3) D4: (1,2,3) B1:…

A: Here we will find poinr D'4 symmetric of D4

Q: Detemine whether the differential eguation iš linear of nonlinear and qve reqsons- Ox*dy txdy= Sinx…

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Q: W = spanR{1, cos² (x), sin² (x)} = R + Rcos² (x) + Rsin²(x) Justify for each of the subsets {1, cos²…

A: Given: W=spanℝ1, cos2x, sin2x=ℝ+ℝ cos2x+ℝ sin2xWe need to justify for each given subsets that it is…

Q: Find the derivative. 26) dx 16t7 dt A) B) 2x5 - 2 C) 16x7/2 D) 8x3 sin t 1 27) du 25 - u2 1 - Cos t…

A: 26) To find the derivative  ddx∫1x16t7dt First find the integral ∫1x16t7dt=16∫1xt7dt…

Q: дz az Use the chain rule to find and Əs Ət əz Əs əz at = = ¹(=), z = tan u = 3s + 5t, v = 5s - 3t

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Q: 2) f(t) = 4t3 sin %3D

A: we have to find Laplace transform

Q: Question: Find Y As A Function Of T If 16y" - 40y' + 25y = 0. Y(0) = 9, Y')O) = 5. Y = . Find y as a…

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Q: Normalize the set of functions "sin, n= 1, 2, 3,...", -d < x < d п d

A: Given: To normalize the set of functions

Q: Let f(x, y, z) = x“y + z* and x = s³, y = st°, and z = s°t. (a) Calculate the primary derivatives ,…

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Q: -3t k Compute the first, second, and third derivatives of r(t) = 3ti + 5 In(t)j + 5e

A: r(t)=(3t)i+(5lnt)j+(5e-3t)k   We are required to findFirst derivative Second derivativeThird…

Q: Jige If f(2) =-3, g(2) =4, f' (2) =2, and g' (2) =, d. then dx -21 16 9. 16 -13 16 29 16 6 jp 3…

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Q: (4-.1.P)an (4-t,t,) and V(t) = (3, t,

A: The given curves are ut=4-t2, t, t2 , vt=3, t2 , t . Let vt=vs →3, s2 , s . Comparing  the…

Q: 7. Which of the following sets of functions is linearly dependent on R0,2? (a) {6, z, sinz} (b) {1,…

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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: In integrating the function f(3x + 5)(cos) dv using integration by parts, what would you choose for…

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Q: For the generating function A(z)=- find the corresponding r≥ 0. 1-9z

A: Given: The function generating function is Az=21-9z2. To find: The numeric function corresponds to…

Q: 3+ 2x² + y², find all second derivatives 5. For the function f(x, y) = v fe: fy and f"y. Show that…

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Q: A Find the value of J G dL if G = x'a, - xyza, given points P,(1,2,3) and P;(5,0,4) and a path…

A: Given: G=x2ax-xyzaz P1:1,2,3 P2:5,0,4   To find: The value of ∫P1P2G·dL for a path consisting of:…

Q: If Y - Exp(2) and Z ~ Exp(3) are independent, what is pdf of W = Y + Z?

A: Concept Sum of independent exponential distribution is gamma variate. Suppose X1, X2...,Xn ~exp(@)…

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: If, for V = V (t), tsin(V) = cos(V)+ In(t), then: a) V'(t) = 1 – tsin(V) t(t cos(V) + sin(V)) b)…

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