Use proof by induction to prove that the recursive form of the sequence equals the closed form given. Recursive Form: a, = an-1 + 62-4 with a1 = 1 %3D %3D Closed Form: 3n2-n- 1

Q: Identify the direction of increase in z in each of the following cases: (a) Maximize z = x1 - X2.…

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Q: Which of the following is a linear system of ODES? Ox' = 7 sin(x) – 7y, y' = 7x – 2 cos(y) - Ox' : -…

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Q: Evaluate the following limits. If needed, enter oo for oo and -oo for -0. (a) lim (38z2 – 38z³) = I+…

A: For a polynomial of the form: P(x)=axn+⋯+bx+c, if a<0, the degree: n is odd, then it can be…

Q: Detal of r=4sin (20)

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Q: f (1, 2) = 3 and the derivative of the function f in the i + j direction at the point (1, 2) is 0.7.…

A: Given that f1,2=3 and derivative of the function f in the i+j direction at the point 1,2 is 0.7. We…

Q: what notation is use to distinguish the sequence?

A: Notation of sequence is as follows:

Q: 2 dy + (1 + log y) dx d?y (1– log y ) dx2

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Q: Are the following series conditionally convergent, ab- solutely convergent, or divergent? Show all…

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Q: Wikle hove 4o% acid solution and we want 75litres of watkr shold we put into the 40% solzution of…

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Q: x = y + Z y² = 0.000396707 - 0.24576 x2 z* = 0.00029753 – 0.12288 x²

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Q: Given the following set of the vectors from M22 1 1 0 0 10 S 0 0 0 1 11 In order to check whether…

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Q: Calculate the power series solution of the differential equation of y'- y=e* up to the five terms. 1…

A: Calculate the power series solution of the differential equation of y'- y = e^x up to the five…

Q: Determine the inverse Laplace transform of the function below. 7. Click here to view the table of…

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Q: 15) Solve the following by constructing the truth table (determine whether valid or invalid): Q→-P…

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Q: R.2. Let X be the collection of all functions f :R→R. Show that there exists a one-to-one function G…

A: It is given that X is the collection of all functions f: ℝ→ℝ. Show that there exists one-to-one…

Q: J (5x)sin( nn : 1.5 )dx + , (5x – 15 )sin NT X 1.5 dx 1.5

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Q: 8. Let (X, d) be a metric space, and A, B are subset of X, then (i) Fr(A) = A n (A)° = Ā – int A…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Apply the 1t derivative property to : 1) f(t) = e-2tsin5t 2) f(t) = = cost sint 3) f(t) = e²tsin2t…

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Q: dy Given a first order differential equation dx 3xy + tan y x'+xsec? y Q3 (а) Clarify the exactness…

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Q: c). i. Find the general solution to this homogeneous equation using the auxiliary equation method…

A: We will use the basic knowledge of differential equations and methods for solving them to answer…

Q: Hence, write down the associated modal matrix P and diagonal spectrum matrix D, and use these to…

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Q: Let n be a positive integer. Which among the following statements is true? n + 1 and n + 2 are…

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Q: An object ol nass 10 kg is toloased trom rest 4000 m above the ground and allowed to fall under the…

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Q: Find all the values of x such that the given series would converge. (-1)"(х")(п + 7) (4)" n=1 The…

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Q: Solve the following differential equation y" +2y'+y=x-1 Select one: O a. YG.S= C,e¯+cze¯2X+x-3 O b.…

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Q: Hind the equetion by eliminatig the corresponding rectanguar paremele

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Q: Determine whether the argument is an example of inductive reasoning or deductive reasoning A…

A: Make  a table as follows based on given data 1. Colin played Football Therefore write Football and…

Q: Problem 4: Use theorems on limits (limit laws) EXCEPT for the polynomial function rule, to get the…

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Q: b) Consider the following mixed constrained LP problem. Minimize z = 4x, + x2 Subject to 3x1 + x2 =…

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Q: 8. If n+1, 2n-1 and n+5 are in AP. Find the value of n

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Q: Let T:R'R? Linear trans formation in the form T(X,4,Z) =(X+24,0,32) grand fatherokert ☺ Img 3.

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Q: Find both the sum and difefrence of Matrix A and В. 4 -6 A = 6. 15 B= 11 - 23 -12 3 51 35 -4 71 52…

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Q: Give an example of a set S which is (i) bounded above but not bounded below, (ii) bounded below but…

A: (i). We consider the set which has bounded above but not bounded below

Q: dx ,2 /9 – x² 2

A: Solution

Q: Give an example of a set S which is (i) bounded above but not bounded below, (ii) bounded below but…

A: (i). We consider the set which has bounded above but not bounded below

Q: 2. When object P, with mass m, , moves at v, and object Q, with mass m,, moves at v,, the velocity…

A: Given,For P, mass = m1  and velocity = v1Let, velocity after collision is u1For Q,mass = m2 and…

Q: 3. The table below shows the highest daily temperatures (in degrees Fahrenheit) averaged over the…

A: As per the question we are given a data table of the avarage monthly temperature (y1) over the…

Q: Use the method for solving Bernoulli equations to solve the following differential equation. dx X…

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Q: Determine all prime numbers a, b and c for which the expression a² + b² + c² – 1 is a perfect…

A: We have to determine all the prime numbers a, b and c for which the expression a2+b2+c2−1 is a…

Q: A car travels along a motorway and the amount of petrol in it tank is monitored as shown on the…

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Q: find the talor Palynomial Pa), Contered ot co tor

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Q: d d Calculate ri(t) · r2(t)] and [r:(t) x r2(t)] first by differentiating dt dt the product directly…

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Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below y+8y…

A: Laplace transform of the differential equation

Q: Use any variable to rewrite the following sentences to mathematical statements Twice the…

A: Introduction: A variable in mathematics is an alphabet or term that represents an unknown number,…

Q: Derive this expression from first principles. f(R)=3/(bR)

A: Questions from derivatives.

Q: 1. For each situation, tell whether it could be modeled by a linear equation, and explain why or why…

A: To determine which of the given situation can be modeled by a linear equation.

Q: b) Tshepile Wool Company (DWC) operates a large farm on which sheep are raised. The farm manager…

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: To find the domain of r(t) and the value of r(t0).

Q: 38. Solve Find the system of curves satis fying the differential equating x2 1 a2 y² xdx + ydy + c…

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Q: Our aim is to check whether 179 is a prime number or a composite number. Which among the following…

A: A number is set to be prime if the number is divided by 1 and itself Let us consider any number n…