Q14. For each of the following convergent series, find its exact sum. Show all your work ! 3" + (-1)" (b) E(3" - 31/) - 31/(«+1) | (a) 52n+1 n=1 n=1

Q: 1. Let X be the graph of f(r) = r given below that is, X is the subset of R x R satisfying the given…

A: Sol

Q: 5. List the intervals where f is concave up. 6. List the intervals where f is concave down. 7. List…

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Q: Factor these two matrices into A = XAX-1: [1 2] A = X = A = [1 1] A 3 3 X = A = (Note that you must…

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Q: Q2) Find the optimal solution using simplex method Max z = 8x, + 10x, + 7x3 s.t: 4x, + 6x2 + 3x3 5…

A: The problem is max z=8x1+10x2+7x3 subject to 4x1+6x2+3x3≤607x1+2x2+5x3≤406x1+6x2+9x3≤36…

Q: Assume that  dx1/dt= x1(10-2x1-x2) dx2/dt= x2(10-x1-2x2) a) Graph the zero isoclines. b) Show…

A: Given- Assume that  dx1dt = x110 - 2x1 - x2dx2dt = x210 - x1 - 2x2 To find-  Graph the zero…

Q: ttempt to use the Root Test to decide whether the series converges. L = lim lan| n00 of the limit L…

A: In this question, the concept of convergence is applied. Convergence The feature of approaching a…

Q: Find the area of the paraboloid x? + y +z² = 2 by the plane y = 0.

A: The solution is below.

Q: For which value of k does the matrix -3 k A : 7 -1 have one real eigenvalue of multiplicity 2?

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Q: ax+b 2. For the general equation of a rational function in the form f (x) state the x-intercept, y…

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Q: You want to put a 5 inch thick layer of topsoil for a new 31 ft by 28 ft garden. The dirt store…

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Q: 2 - 2] 4 | Let S = 1 -1 1 The basis of S are 2 1 | O (2. 1, 1), (-2, 1, 2) O (2, 1, 1), (-4 .0. 1) O…

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Q: Let v be a vector in R" and define a function T, : R" → R by T,(x) = x v. (a) Show that T, is a…

A: here we can use simple conditions that if a linear function preserve scalar multiplication and…

Q: Solve the IVP. Find and verify the condition num- ber. y' = -ty; 0<t < 5, y(0) = 2, 2.5.

A: The solution is

Q: 2. Consider the equation: dy = y² + 2yt +t² - 2y – 2t – 1 dt a. Find a change of variable that…

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Q: a) ir(A - 1)1- ( -2) %3D Find the matrix A

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Q: 5. nts) Let v1,..., Un be vectors in a vector space V. Suppose w is another vector in V. Determine…

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Q: I-y 1. Let f(r, y) Find: Ity+1 (a) f(2, 1) (b) f(1,2) (c) f(a, a) (d) f(y+ 1, y)

A: Use the given function.

Q: Melissa Sorez, age 42, takes out a $300,000 five-year term insurance policy. What is her annual…

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Q: Evaluate f(1). F(s)= S 4 Round-off to whole number. Answer: 382

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Q: Q4) Find plane area inside the polar function r= 2 and outside the polar function r= sin -e) +1 in…

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Q: Write at least 5-10 sentences essay/discussion on what you can observe on the values in table and…

A: This graph denotes the position of an object at certain time interval and the distance of the object…

Q: 5. Find the inverse Laplace transform of the function as + b H(s) = .а — 9, b — 10, а — 4, В — 3. (s…

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Q: (i) Use Euclid's algorithm to find a multiplicative inverse of 23 modulo 75, and hence solve the…

A: This is a problem of Number theory, counting, and modular arithmatic.

Q: QIn usual to fol @ Is Co,1 ] is Is Lo D .)

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Q: 2 Evaluate the feltowing cartesia

A: Given,        ∫04∫325-x2dydx=

Q: If y is the solution to the initial value problem 9x2 y(0) = 1 2y then 2) =

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Q: (iv) Let be an odd prime number and let r be the rational number 1 1 r = 1+ 2 1 + 3 Prove that p…

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Q: The relative error in reading a galvanometer is given by tanx + cotx, where x is the angular…

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Q: Evaluate F(4). f(t)=sin(2t)cos(2t) Round-off to 4 decimal places. Answer: 0.0625

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Q: Given that

A: Given that           11-x=∑n=0∞xn convergence with (-1, 1). To find the power series 16-x with…

Q: Problem 6 This extreme value problem has a solution with both a maximum value and a minimum value.…

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Q: Compute the integral by the adaptive trapezoidal quadrature method (must use the recursive for-…

A: Given that ∫-22x-13dx by using trapezoidal quadrature h=0.5 x -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 y…

Q: Write the equation in standard form of the circle whose center is at (0, 0) and that is tangent to x…

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Q: Az + 2xy²)dx + (cos y + 2x²y)dy = 0

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Q: ExercisesS 1. Construct the truth tables for the following compound statements: (a) p^ (q V r). (b)…

A: As per the policy of bartleby the provisions is to solve only three sub parts

Q: Question 11 Let k be a real number and let ( be the line whose equation is given by 1 1 +t teR. k If…

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Q: [1 2 3 Problem 1. For this problem, let A := |0 1 0 2 1 2 WeightedOrderAlgjava - Notepad File Edit…

A: Given that A=123010212 (a)From the definition of the eigenvector v corresponding to the eigenvalue λ…

Q: 99. How many full gallons of regular lead-free gas can Josie buy for $20? GAS PUMP Regular Lead-free…

A: Given in question,  Regular Lead free  = $1.69

Q: Compute the line integral -xdy + ydx 2(x-y)2 +4xy where L is the circle (1-x)2 + y2 = 3 with a…

A: We can write the given line integral as ∫L y2x-y2+4xydx+-x2x-y2+4xydy, where L is the circle…

Q: 4. Evaluate the iterated integral: E dydr. 1/4

A: Double integral

Q: For an n × n matrix A, we can similarly define the matrix exponential aseA = I + A + (1/2!)A^2 +…

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Q: sin x – e-* = 0, [0,1]

A: Given sinx-e-x=0, 0,1

Q: Question 4. Use Taylor's Theorem to estimate sin(3) to within 1/60.

A: This is a problem of series approximation.

Q: hw.2 Evatuate the fotawing cartesian integrats by changing theminte equivalent Pala integrals: dy dx

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Q: N-1 N, k-r = mN, m an integer | Se-i(27/N)(k-r)n n=0 0, otherwise

A: To prove: ∑n=0N-1e-j2πNk-rn=N,k-r=mN, m is an integer0,otherwise

Q: evaluate t-0.01, Given: 21' + 201 = 100, I(0) = 0 Round-off to 3 decimal places. Answer: 0.476

A: Laplace Transform or Inverse Laplace , solution of the intial value problem

Q: 2 V4-x? xy dyd. + y? а. x² 0 0 V

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Q: +5s+19 (6?+4)(s²+9) Find the inverse Laplace of O a. cos(3t)- cos(2t) -음sin(2) + 음sin(36) sin(2t)…

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Q: A tank is discharging water through an orifice at a depth x (m) below the surface of water whose…

A: Simpson's 1/3 Rule: Let f(x) be a function defined on a,b, then the Simpson's 1/3 rule is given by:…

Q: An engineer who accidentally inhaled poisonous fumes was given treatment for it. The concentration…

A: Let us solve the given question by method of least square in the next steps.