7. Find f(4) if f is defined recursively by f(0) = 2, f(1) = 3 and f(n+ 1) 4f(n) -3f(n-1)

Q: Find a closed form representation for the function defined recursively by ƒ(1)=4 and f(n)=3f(x)+n.

A: This is a question of recurrence relation and time of complexity.

Q: 8. Theorem 1.7.4 x -le* dx is convergent if and only if n > 0.

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Q: Let {(=) = In ="(z +2)*(z² + 9)] f'(x) =

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Q: Min z = 4x1 + 2x2 s.t. 3x1 + x2 ≥ 27 -x1 - x2 ≤ 21 x1 + 2x2 ≥ 30 x1 and x2 are unrestricted .

A: the given LPP is as follows Min z=4x1+2x2 subject to  3x1+x2≥27-x1-x2≤21x1+2x2≥30 where x1,x2 are…

Q: 1) Find the final value of the sequence {Xk} with Z-transform of F(z)= Mz2-z , where M is any %3D…

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Q: The t-table has entries for areas of 0.10, 0.05, 0.025, 0.01, and 0.005. In contrast, the χ2-table…

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Q: Show that an = 1/2n + 1 is decreasing.

A: Given: an=12n+1 Substitute 1 for n in the equation an=12n+1. a1=12(1)+1=13=0.333

Q: 5 Prove for Vx > 0 0<1+x - 1 x + - 81 1/9 1/3

A: Prove for ∀ x&gt;0  0&lt;1+x3-1-x3+19x2&lt;581x3

Q: 1. Determine the z-transform of the sequence x(n)={2,1,-1,0,3}

A: Since you have ask more than one question, we will answer the first one. If you want other question…

Q: Prove that 2 1 1 5 2 (4-2x)² for all relevant x-values

A: We have to prove that 1215-x&gt;24-2x2, for all relevant x-values.

Q: 23. Find the first 3 iterates of the function f(x) = 0.75x when o = 5. %3D O 3.75, 2.8125, 2.109375…

A: Explanation of the answer is as follows

Q: 1 Expand f(2) = -in the domain 4 < |2 < 12 (z-4)(z–12)

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Q: There is one male baby seal for every nine female baby seals. Let X be the number of male baby seals…

A: Let p=P(male baby seal) = 1/9 Here n=5 Note that X follows a Binomial distribution with n=5 and…

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Q: 2.59 Find || f |sup if a) f(x) = x on (-1, ). So if x E Q, b) f(x) = – x² .2 if x ¢ Q. -

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Q: 1 Expand f (z) = in the domain 4 < |z| < 12 (z-4)(z-12)'

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Q: 8. There is a jump discontinuity at x = 2 and f(2) = 3

A: Follow the procedure given below.

Q: Q2/ Find the final value of the sequence {} with Z transform 4z²-z F(z) %3D 2z2-3z+1

A: Given: The given function is Fz=4z2-z2z2-3z+1

Q: Discuss the Convergence or Divergence for D { [4+ (-0"]" (Z+2)" こう 2n+1 - DZ² 2 لع Wi ngo (2n+¹)!

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Q: 1 Expand f (2) = in the domain 2 < |z| < 14 (z-2)(z-14)

A: Follow the procedure given below.

Q: What is the expansion of 1 f (x) = %3D Ο Σε' Σ 2n 2n Σ Next

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Q: Find the second order Taylor polynomial near x = 3 of y" – (x –- 2)y' + 2y = 0 with the initial…

A: Your question has two parts belonging to two different subject categories. Your first part on…

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Q: 6) Show that the function f:Z → N given by 2n +1, n20 f(x) = -2n, n<0. is 1-1 and onto. I

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Q: Theorem 1.7.2 [ x-'(1– x)" -dx is convergent if and only if m > 0 and n> 0. Scanned with CamScanner

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Q: Q1) check the continuity of fX) at X- -1, 0,1.23 -1<x<1 2x-1, 3x-2 25x53 2, x=3

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Q: Give a recursive definition (with initial condition(s)) of (an) where (n = 1, 2, 3, . . . )

A: We have, an = 212nWe have to find a recursive definition with initial conditions of an starting from…

Q: 2. (a) Use the definition of the derivative and the Binomial Theorem to = nx"-1 for any x" is f'(x)…

A: Since you have asked multiple question, we can solve first question for you. If you want other…

Q: II) Classify the PDE (1 + x)²Uxx - 4xUxy + Uyy = x.

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Q: (х — т 11- тх if x < 3 if x 2 3 5) Find m so that g(x) = Is continuous for all x?

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Q: Show that the generating function for compositions into an even number of parts, each of which is…

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Q: Suppose that the function f(x)= qx<+4x-6 satisfies the necessary conditions of Rolle's theorem in…

A: The given function is f(x)=qx2+4x-6 ....................................... (1)  Satisfied the…

Q: Q2/ Find the final value of the sequence {xk} with Z transform 4z2-z F(z) %3D 2z2-3z+1

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Q: 3. Show that f(2) = (z+ 1)³ – 3z is nowhere analytic.

A: The given function is, fz=z+13-3z The function z is given by, z=x-iy Substitute values in above…

Q: Compute f' (3). f (x) = –3.3x² + 3.9 O f' (3) = –19.8 %3D O f' (3) = –3.3 f' (3) = -15.9 O f' (3) =…

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Q: Q2/ The sequence {xk} has the Z transform F(z) 3z(z-1) z3-2z2-4z+8 Find {xk}

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Q: 4. a) Suppose that for some specific problem, heuristic function h is admissible. Is h? admissible?…

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Q: - 4x³| [x-2x] ,1s x<2 Os x<1 Let f(x) = Then discuss the differentiability of f(x) in (0,2) Here []…

A: Given that: f(x)=|1-4x2| ,    0≤x&lt;1[x2-2x] ,      1≤x&lt;2

Q: What is the run-time complexity of the of the recursively defined Closed form function T(n)=3T(n-1)…

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Q: determine convergence or divergence by any method.

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Q: any n > N(\epsilon) | fn(x) - f(x) | < \epsilon

A: The Weierstrass approximation theorem states that every continuous function defined on a closed…

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Q: 1 Expand f (2) in the domain 4 < z < 12 (z–4)(z–12)

A: Introduction: The Laurent series of a complex function f(z) is a representation of that function as…

Q: 8. Find a closed form representation for the function defined recursively by f(1) = 10 and…

A: Definition: Here is the master's theorem for recurrence relation is follows, Tn=aTnb+cnk, T1=c1…

Q: Find the linearization at x = a. f(x) = a = 7 (Express numbers in exact form. Usc symbolic notation…

A: Linearization L(x) of the function f(x) at x=a can be written as below: L(x)=f(a)+f'(a)(x-a)

Q: 6. Verify that fy =fx for the following func %3D ху 6.4 5. 3 f(x, y) = 2x°y* - 4x°y³ f = fy=. fxy =…

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