Show that the series 71 n' (2n)! is convergent. Deduce that lim 0% (2n)! n=1

Q: 32 128 The series 3 is equal to .....(Correct to 3 decimal places) ... 33.3 35.5 37.7

A: Note: The maclaurin series expansion of tan-1x is: tan-1x=x-x33+x55-x77+...

Q: Determine whether the sequence Ve" + 3" converges or diverges. If it converges, find its limit. O 1…

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Q: (2n )! | [P, (x)]° dx | (1-x?)" dx %3D 22" (n!)2 -1

A: Solution

Q: x+y3 Consider lim Which ONE of the following statements is TRUE? (.y)- (1, -1) x+y A. None of the…

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Q: 9. Use the series solution to solve the problems. a. xy" +4y'-xy = 0

A: Since you have posted a multiple  question according to guildlines I will solve first   question…

Q: Consider the following IVP: x" - 4x' + 4x = 4e2t; x(0) = -1, x'(0) = -4 %3D %3D

A: We have to solve the given differential equation,(IVP).

Q: 2s +3 d the Inverse Laplace Transform of (s+4)

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Q: Find the g.c.d. in Z [i] of 2 and 3+ 5i.

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Q: For x, y E [0, 1], prove that 1 xy(1 – x – y) < 27

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Q: Use X = X + X, = eAtC + eAt e-As F(s) ds to find the general solution of the given system. Jto 10 X'…

A: Given x'=1004x+te6t

Q: What is the particular solution to the differential equation +1+y = 2e- with y = 1, 2=-1 when x = 0?…

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Q: Given the function f (x,y) =/(x²– 4)(y²– 9). Which ONE of the following statements is TRUE? O A.…

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Q: For x,y E [0,1], prove that xy(1-x-y)≤1/27

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Q: C has equation 2x2 +y2 = 18. Dete l passes through the point (1, 0). %3D

A: In this question, the concept of the derivative is applied. Derivative A derivative can be used to…

Q: For the curve defined by F(t) = (e¯', 4t, e') find the unit tangent vector, unit normal vector,…

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Q: The power series solution of the differential equation y" + x y = 0 has a solution of the form Ca (1…

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Q: fn (x) = Vx e (1, 00), Vn E N. Explain why the sequence {fn} does not satisfy the conclusion of the…

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Q: FIND THE MALLAURIN SERIES for flx) L DEFINITION oF A MALLAUREN SEREs, AssumE

A: Introduction: Let f(x)=∑n=0∞an be a series, then the series will converge if L&lt;1, where…

Q: he line connecting PC to PT is equal to 125m. If this line makes an angle of 13.5 with the back…

A: Given step by step explanation below

Q: and y=0 (roune

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Q: In Exercises 29-32, a solid is described along with its density function. Find the center of mass of…

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Q: the value of JA

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Q: What is the general solution to the differential equation (tan x)dy – (4y In y – y tan³x)sec²x dx =…

A: We will convert given differential equation into linear differential equation by appropriate…

Q: Plot the complex number on the complex plane and write it in polar form and in exponential form.…

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Q: 3. Given the parent function f(x) = |x|, write the equation of the function g(x) whose graph is…

A: The graph of a function f(x) is the ordered pair of points (x,y) in the cartesian coordinate system…

Q: 2. List the amplitude, midline, and period of each of the following functions: (a) 3 cos(T/4 * x) –…

A: We will use standard form of equation  For y= a sin (bx+c) +d           or     y= a cos (bx+c) +d…

Q: ular inte 1 3 te

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Q: Let f(x) = X" and g(x) = x3 f (x2/25). Let anxn be the Taylor series of g about 0. The radius of…

A: Given function is fx = ∑n=1∞ xnn  and  gx =x3  f x225 Note:- x225 =x52

Q: Suppose a test has sensitivity 0.787. The test also produces false positives at the rate of 17% when…

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Q: aplace transform of –

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Q: The admission fee at an amusement park is $10.75 for children, $16 for adults, and $15 for seniors.…

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Q: Establish that if a is an odd integer, then 2" a“ = 1 (mod 2" *2) for any n 2 1.

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Q: Question 22 Which of the following expressions is a closed form of the sum of the expression (i +…

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Q: 4 – 3/k k2 - 2k k=3 the Integral Test be used for this series? Explain in detail your a

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Q: For the following ordinary​ annuity, determine the size of the periodic payment.   Future Value…

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Q: What value of x is in the solution set of 2x – 3 > 11 – 5x

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Q: he price-demand equation of the particular brand of shampoo át á šúþérmarket chai hen the demand is…

A: Note- Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Ikeoluwa collected data on whether 65 professional golfers have practiced for at least 10,000 hours…

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Q: (b) Obtain the first five terms of the Series solution y(x) = anI" to the IVP /(z) – y(x) = r with…

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Q: Find the upper quartile of the following set scores: 1, 3, 4, 5, 6, 8, 11, 13, 17

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Q: Use variation of parameters to solve the given nonhomogeneous system. X' X - -7t e X(t)

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Q: (circle one of the following choices) b) a) The primary trigonometric ratios b) The sine law c) The…

A: We need to solve the triangle.  Primary trigonometric ratios can be used when we have a right-angled…

Q: What is the particular solution to the differential equation * + (1 + x)y = 12 with y 0 and = 0 when…

A: The solution is given as

Q: none of these options OR={(0,0), (1, 1), (1, 3), (2, 2), (3, 1), (3, 3), (4, 4) } OR= { (0,0), (1,…

A: Introduction: An equivalence relation is a type of binary relation in mathematics that should be…

Q: 4. Let F(n) = 2F(n – 1) + 5F(n – 2) – 6F(n – 3) with initial conditions F(0) = 4, F(1) = –4 and F(2)…

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Q: The differential equation cos y dx + (cos° y – x sin y) dy= 0 has a solution of the form f(x, y) =…

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Q: Find the Taylor polynomials po, P1, P2 and P3 for f(x) = Inx at x = 1. Use a graphing utility to…

A: Answer :-

Q: 4. . Evaluate the Laplace transform of the function t S, sintdt

A: The solution is given as

Q: Express the iterated integral as an equivalent integral with the order of integration reversed. 28 4…

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Q: The domain and the range of z=cosh x+y are represented respectively by D={(x,) ER X R: and R=(- 00,…

A: Domain is set of points where function is defined , range is image set of function.

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.