Explain why if an converges, then limn→∞ an = limn→∞ an+1 . I need explanation why this theorem holds , not only proof.

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A: The given problem is to determine the maximum and minimum directional derivative of the given…

Q: Find the future value of an annuity due of $2000 paid at the beginning of each 6-month period for 8…

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Q: 1. Evaluate the following integrals: (a) [182³ s 1825 sin (92²) dr (b) Sa 7 1 dx z ln²₁ √I

A: ∫18x5sin9x2dx Let 9x2=z dz=18xdx…

Q: 4. Let A and B be sets. Prove that AB in each of the following. (i) A = {x²: x € Z} and B = Z A = R…

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Q: Consider a propositional language where P: x is a prime number. Q: x is odd. Which of the following…

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Q: Graphing Quadratics Standard Form Identify y-int, x-int(s), axis of symmetry, vertex from the…

A: The given equation of  parabola is y = -x2 +6x -5 To find the point of y-intercept, we have to put…

Q: Generate solution of the higher-order differential equations using different analytic techniques.…

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Q: Evaluate the following integral, xyz dS, a where S is the surface with parametric equations x = u…

A: Introduction: You essentially already understand surface integrals if you are familiar with double…

Q: Suppose that start of month payments of $376 are made to an investment that earns interest at the…

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Q: (c)mm [ex ₁F₁ (a:c:x)]=(-1)" (c-a), e¯* F₁ (a;c+m;x).

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Q: [7] Find the solution around x = 0 of the differential equation (x - 1)y" + xy - y = 0. Find the…

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Q: Can anything be said about the speed of a particle whose acceleration is always orthogonal to its…

A: Given: Acceleration and velocity of a particle are orthogonal to each other. We need to check what…

Q: You have $300,000 saved for retirement. Your account earns 7% interest. How much will you be able to…

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Q: Generate solution of the higher-order differential equations using different analyti echniques.…

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Q: thun no in

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Q: Q2: Evaluate the following 8 b) fo e-x³ dx

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Q: 1 Use the Mean Value Theorem to show that 1+x 0.

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Q: Select the one true statement. Consider a C function f: R" → R and two multi-indices a,

A: To solve this problem I will use the fact that every polynomial in any variable is smooth function.

Q: The curve C is the circle of radius 7 contained in the plane z = 7 and centered around the z-axis,…

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Q: [ [6z³ cos(2a³) + 3x³ sin(22³)] da

A: We solve the given integral by substitution and then integrating by parts. Integration by parts:-…

Q: Find a sequence (on) of characteristic functions with the property that the limit given by o(t) =…

A: Given Data: Here we have to find a sequence ϕn of characteristic functions with the property that…

Q: Set up the integral that solves for the area of the shaded region (a) using a as the variable of…

A: We can find the area of the shaded region.

Q: Find f(t) for each of the following functions: 6(s + 10) (s + 5)(s + 8) a) F(s) =

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Q: A. Using the Borda count method, who is the winner? B. Is the majority criterion satisfied? Why or…

A: We have to find the highest winner score

Q: B. Evaluate the following limits: i. ii. lim tan-¹(x4 - 4xy + y²) (x,y) →(1,0) lim (x,y) →(0,0) COS…

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Q: Determine the convergence or the divergence of the series: 00 n=1 1 + n lnn n² + 5

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Q: Show that 80 n=1 -15 is divergent without using any of the tests you have seen so far. Use the…

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Q: 1) a) Use the Taylor theorem for the function U(x, t) = text with the step size Ax (t, is held…

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Q: Use the Algebra of Limits of Convergent Sequences and Example 9.5.1 to prove that for any c ER, as…

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Q: The equation: 3x - 4y = 5 represents a line. What is the distance of the line to the origin? Round…

A: The perpendicular distance of the line ax+ by + c= 0  from origin is given as |c| ÷ ( √(a2+ b2))​

Q: The inverse Laplace transform of 4s² 44s + 130 (s - 3)(s² - 14s +50) is: peat - +qeßt cos(wt) + rest…

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Q: 15. Let C = {(2n + 1)³: n E R} and D = {2n + 1: n E R}. What is the relation between these two sets?…

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Q: Given that the Laplace transform of f(t) is F(s) = s 5 s2-3s +3 then the Laplace transform of…

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Q: Use Laplace x(3) + x - 56x' = 0; x(0)=0, x'(0) = x''(0) = 3 transforms to solve the following…

A: Introduction: Differential equations are resolved using the Laplace transform. It is generally…

Q: Evaluate the triple iterated integral. TT/2 'π 15 6² 6² 6² --- ³² 10 e-p³p² dp de do

A: The given problem is to evaluate the given triple integral with given limits of integration.

Q: ppose that a and b are odd natural numbers and a² + b² = c². Prove that c is irr

A: We can prove for irrational.

Q: 1. Suppose a, ne Z and 0 < a <n. Prove that n- n- (12) - (^= ¹)+(2²=1) a a- in two different ways:…

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Q: Write the system of linear equations in the form Ax = b and solve this matrix equation for x. X1 2x2…

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Q: Use a change of variables to find the volume of the solid region lying below the surface z = f(x, y)…

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Q: The biological relationship between the growth for the fish population and the size of the fish…

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Q: SOLVE STEP BY STEP IN DIGITAL FORMAT In the parabolic reflector, the light source is placed at the…

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Q: Let τ and τ' be two topologies of a set X. Is the family τ∪τ' formed by the open elements of both…

A: Union of two topologies is not necessary a topology.

Q: Generate solution of the higher-order differential equations using different analytic techniques.…

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Q: 4. Describe, with examples, how differentiation, limits and integration are used in real life.

A: To Explain: Real life examples of Limits, differentiation and integration.

Q: Find the intervals of decrease and increase for the function TC f(x) = c --- X

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Q: Determine convergence or divergence of TL A. converges B. diverges M 7n +6

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Q: Follow the following steps to find all three roots of the equation x³ + 3x² - 6x + 20 = 0. (a) Use…

A: Given: The cubic equation is given as x3+3x2-6x+20=0.

Q: Compute the n x n determinants: X a a 8 a (a) a a a x ⠀⠀ : a a a ... ... 000 000 a X " (b) -t 0 1 -t…

A: As per our guidelines we are supposed to answer only first question, kindly repost other parts in…

Q: Dario invested $5,990 in an account earning 5.17% p.a.How many days did it take for his investment…

A: Total investment P=$5,990 rate of interestr= 5.17% p.a Earning on interest C.I=$171.5

Q: Generate solution of the higher-order differential equations using different analytic techniques.…

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