First order difference equation Consider the simple model |y(t)+ay(t-1)=bu(t-1) ÔN Σy²(t-1) -Σy(t-Du(t-1)] -Σy(t-1)u(t-1) Σu²(t-1) HIE -Σy(t)y(t-1)] Σy(t)u(t-1) Exercise: Suppose for t=1 to 6 the value of u and y are: u=[2 3 2 5 3 7 y=[-23 48 -93 188 -371 745 Derive N

Q: (a) Find all equilibria of N,, 1 = 1.4N,, t= 0, 1, 2,.. (b) Use cobwebbing to determine the…

A: Given: Nt+1=1.4 Nt ;  t=0,1,2,...

Q: (6,8,-5) Evaluate the integral (65) y dx + x dy +4 dz by finding parametric equations for the line…

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Q: Can you show part b how to solve and more details

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Q: (6) Find the orthogonal trajectories of the family of curves r= 2C cos 0, where C being parameter.

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Q: can you explain how they simplified using the chain rule

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Q: Chapter 12, Making Connections, Question 002bi Use the fact that N (t) can be expressed directly in…

A: Use : u(t) = f(t)i + g(t)j + h(t)k u'(t) = f'(t)i + g'(t)j + h'(t)k  u''(t) = f''(t)i + g''(t)j +…

Q: (а) Т F The order of the equation y(1 + (y)²) = 1 is 2. dx (b) Т F The relation ry + eª = x³ is an…

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Q: Graph of f

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Q: b) Find f(")(x) is S(x) =

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Q: ^ ^ Find T, N, and x for the plane curve r(t) = -6 In(sec t)i – 6tj. − <t< (t)=)i+j Type exact…

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Q: (i) If f(x, y) = sin (ry2) and x³ + y² = 2xy, find expressions for the partial derivatives of/0x and…

A: To calculate partial derivative of  with respect  , we keep the other variable constant.

Q: • Let S be the graph of f(r, y) = r² + y² – 2r + y for (r, y) E D = {(r, y) :2² + y² < 4 and z + y 2…

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Q: then A(-2u - 20) = -2 ---B 5 and Au 3 Au = 2 4

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Q: We know that: Theorem (*) If y₁, y₂ are linearly dependent on some interval, and their derivatives…

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Q: 6. Find the fized point of flx) [-,1] where', on fa = (동) x-(올)x3

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A: Let (a,b,c) be any element of R3, then (a,b,c)=(x,y,0)+(0,y,z)=(x,2y,z) ⇒a=x, b=2y, c=z ⇒a,b,c∈R ⇒…