Recursive sequence Give a recursive definition of the sequences below. (a) {an}-1 where an = n(n + 1) for all n. (b) {bn}n€N where bn = 2+ (-2)" for all n.

Q: 3) Let f:R - R be defined as: Vx = (x, X2, X) € R f(xi,X2, x3) = 7(x- x) + 3(1- x2) + 6x . a. Is f c...

A:  Given:Let f:R3→R be defined as: ∀x = (x1, x2, x3)  ∈ R3  f(x1, x2, x3) = 7(x1- x2)2 + 3(1 –x2 )2 +6...

Q: Divisibility Prove that if alb and bla, then a = b or a = -6.

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Q: Problem 1. Give an example of a normed space E and a convex function p:E - R such that p is not lowe...

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Q: What would you do in order to solve the following equation 4b=20

A: Given equation is 4b=20. We have to solve the given equation. Divide both sides by 4 and further sim...

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Q: List the eigenvalues of A. The transformation x-Ax is the composition of a rotation and a scaling. G...

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Q: g(t)= 2e"u(t – 1) p(t) = 6[u(t – 2)– u(t –4)]

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Q: Given the function below

A: Given,           f(x)=-162x3+8913

Q: Find the directional derivative of f(x, y, z) = xy² + yz° at P(1, –1, 1) in the direction of a = î +...

A: The directional derivative of the function f(x, y, z)  at point P in the direction u Find the gradi...

Q: tind the pen meter 4 4

A: As all the four circles have same radius which is 2so the given figure is a square whose perimeter i...

Q: 12. (a) For n = 3, explain why %3D Lo(x) + L1(x) + L2(x) + L3(x) = 1 for all x. Hint: It is unnecess...

A: The complete solutions are given below  

Q: Evaluate x2/3 from x0=1.2 and xn=2.4 of order 3 using Simpson's 3/8 R.

A: This is a problem of Numerical Analysis.

Q: Determine a3 of the periodic function as shown. Round-off to the nearest ten thousandths places.

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Q: Find the solution of the system of linear equation and the value of the determinant of its coefficie...

A: The system of linear equations are:w+2x-y+z=6-w+x+2y-z=32w-x+2y+2z=14w+x-y+2z=8We have to find the d...

Q: PROBLEM: lim CSch 2 ATTEMPT: CSch csch x In %3D Ix1 _csch x = In I+ (0)= In ! (히 %3D In Ito 4. 101 1...

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Q: Find the equations of inequality that has the following graph as the solution. 8) a) b)

A: This is a problem of LP, graphical representation and inequality.

Q: 4. Find the values of w, x, y, and z using Gauss-Jordan Elimination 1 5 -2| 7 3 2 0 |12 2 -2 0 3 5 -...

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

Q: 5. f (t) sinh 3t + cosh 3t – 2t3

A: This is a problem Laplace Transform.

Q: 5. Divisibility Prove that if alb and bla, then a = b or a = -b.

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Q: Consider the mass is obtained by rotating the shaded region, as shown in figure, about the y-axis. A...

A: We will use shell method to find volume of region which created by  rotating the shaded region about...

Q: Find the function f(x) = Ca whose graph is given. f(x) = (x, Y) = (-3, ) 40 %! 27 (x, y) (0, 5) y 10...

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Q: Change the Cartesian integral to an equivalent polar integral and then evaluate: I = 5 N225-y" (x² +...

A: The general form of a double integral is given by ∫ab∫h1(y)h2(y)f(x,y)dxdy, where f(x,y) is multivar...

Q: f(r.y2)4ry t and u is the unit vector in the direction of (4, 2,-5), men the drectional denvative at...

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Q: Calculate the volume of the solid obtained by rotating the area bounded by f(x) the x(x + 1) X-axis,...

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Q: Give some examples of differentiation, linear and non linear in real life situations (preferably in ...

A: Differentiation 1)To calculate the profit and loss in business using graphs. 2)To check the temperat...

Q: how detailed solution for all. Provide the Maclaurin series expansion of f (x) In(3 – 2.r) Find its ...

A: Macluarin series expansion

Q: Solve the equation, d²x + w?x(t) = 0 dt? subject to the conditions x(0) = A and x'(0) = 0 %3D %3D

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Q: Determine whether each of the following statements is true. If true, prove it. If false, give a coun...

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Q: f(t) = sinh 3t + cosh 3t − 2t3 Find the Laplace transform

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Q: = In(2- sin z) with Given sin z + e -2 0. Using the rearrangement z z0 = 0.5. what is the value of #...

A: The fixed point iteration method is a step-by-step method to find the approximate solution of the tr...

Q: The curve C is the circle of radius 5 contained in the plane z 5 and centered around the z-axis, ori...

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Q: VI. Give the Maclaurin series expansion of f(1) = In(3 – 21). Determine its interval of convergence....

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Q: 1. f (t) = t² - 3t + 5

A: Laplace transform of the function by using definition

Q: 7. Check if the following graphs G and H are isomorphic. G: H:

A: Given the graphs G and H below.

Q: 10 The straight line / has equation r= 2i-j-4k +A (i+2j + 2k). The plane p has equation 3x- y+ 2z = ...

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Q: Find the Laplace transform of the following using Direct Integration. 1. L = {t³}. 2. L = {t²e*}. 3....

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Q: Q3. 3 Points A and B have coordinates (-1, 2, 5) and (2, –2, 11) respectively. The plane p passes th...

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Q: 9. Let I = {A1, A2, A3} where A_i={1, i-1, i+1} for all i = 1,2, 3. Then |UT| = 6.

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Q: a b c d е f g h e 8 8. 7 7 6. 4 4 金曲 3 1 a b c d е f g 土 2.

A: how white can escape from the check .Don’t forget:move ,block or capture

Q: Proposition 5. Consider the function f : Z² → Z² defined by f(m, n) = (mn, m+n). The function f is n...

A: Remark: Let f be a function from a non-empty set A to another non-empty set B. Then f is Said to be ...

Q: The value of c such that = 1 is ce o

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Q: A group of college students was surveyed to determine their favorite class among History, Mathematic...

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Q: f (t) sinh 3t + cosh 3t 2t3 -

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Q: Proposition 9. Let n be a non-negative integer. Then 1+2+4+ 8+ ...+ 2" = 2"+1 – 1.

A: see the attachments below

Q: f(t) = find F(4s)

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Q: d. P = 4x1 – 2x2, Q = 2x1 + 6x2; D is the interior of the ellipse: x1 = 2 cos 0, x2 = = sin 0, 0 E [...

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Q: For Exercises 7 through 12, determine whether the distribution represents a probability distribution...

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Q: 2. Recursive function Let g : N Z be defined by g(0) = 2 and Sg(n – 1) if n 2 1 and n is odd, | 29(n...

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Q: log (1 + ax) 1+ x? dx and hence show that =. Evaluate 0, ' log (1 +x) dx = log, 2. %3D 0, 1+x

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