00 If the series a x" +1 -has the radius of 5, then the radius of convergence of the "n+1 n=1 series a x" is equal to ..... n=1

Q: Find the general solution of this ODE: d'y dy + 4- + 4y = - 7t + 5 dt? dt The solution will be of…

A: The solution is given as

Q: The steel beam of uniform T-section shown in Figure Q3(b) is simply supported over a length of 2.5 m…

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Q: Find the solution. (D2-4D +7)y = 0 y = e-2(c,cos3x +c,sin3«) Oy= e"(c,cos/Zx+c,sin/2x) O y-…

A: Given differential equation is (D2-4D+7)y = 0

Q: Find the Inverse Laplace Transform of (s+4)3 A ³(2cos21 + - sin2t) e-2(cos21+ -sin2t) (2cos21 +…

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Q: Find the distance between m [-2, 3, 2,0,3, – 13, –5] and n = [4, –1,1, –5, 0, 11, –3].

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Q: 36 for 0 <= u <= 6 and 0 <= v <= 2(pi) where <= is less then equal too where pi = 3.1415

A: Introduction: An ellipse is the locus of all points that satisfy the equations.x = a sint,  y = b…

Q: Find L10 of the function f(x) = 3* – cos (nx) on [– 3,2]. Explain the Summation Notation you will…

A: here we will find left Riemann sum  ∫abf(x)dx≈∑i=0n-1fxi*Δx    where  Δx=b-anand  xi*= a+i×Δx…

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: 1 Find the Inverse Laplace Transform of s2+2s+ 10 (A -e "cos3t 3 1 B -e -'sin9t 3 3r -e"cost D -e…

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Q: prove that - Every groupof order y i's cyclie.

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Q: 2. Use zero- through fourth-order Taylor series expansions to predict f(2.5) for f(x) = ln x using a…

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

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Q: 2. Verify, without using the matrix for 0(), that [O()]° is the identity matrix 1 0 0 1

A: This is a problem of rotation of the matrix.

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: 1 In solving the antiderivative of f(x) = 2 – sin(x) by miscellaneous substitution, the substitution…

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Q: Vater fills a bathtub at a rate of r(t) liters per minute (where t is the time in minutes). sr(t) dt…

A: Given that Water fills a bathtub at a rate of r(t) liters per minutes where t is the time.

Q: Q2/_solve the following Ordinary Differential Equation by Laplace transform: y" – 6y' + 9y = y²e3t,…

A: Given differential equation is y''−6y'+9y=t2e3t and y0=2, y'0=17. We have to solve the given…

Q: ()* + dy What is the general solution to the differential equation y = 0 ? dx In(1+ Ay) = Ax + B y2…

A: We have yd2ydx2-dydx2+dydx=0 Let dydx=p Then d2ydx2=pdpdy So, yd2ydx2-dydx2+dydx=0 becomes:…

Q: For the following relation ~ on set X, determine whether it is symmetric, transitive or reflexive.…

A: For all x in X, x2 ≠ x2 + 1,hence x ~ x Hence ~ is reflexive.  Now consider the equation          x2…

Q: Show clear and detailed solutions • Determine and draw the graph of the following equation in R³ : z…

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

Q: What is the particular solution to the differential equation x + (1 + x)y = 12 with y = 0 and 2 - 0…

A: The solution is given as

Q: Prove: for n > 1, F; – Fn+1 Fn-1 = (-1)".

A: F_n are the Fibonacci numbers which are defined by F_0=1,F_1=1 and F_n = F_{n-1}+F_{n-2} for…

Q: (D3 - 3D - 2)y =0; when x =0, y=0, y' = 9, y” = 0.

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Q: .Use the Monotone Convergence Theorem to show that the (2n)! {a)" is convergent.

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Q: ) Using the same universal set, find the set specified by each of these bit strings. (i) 11 1100…

A: It is given that U=1, 2, 3, 4, 5, 6, 7, 8, 9, 10. We have to write the elements of the set specified…

Q: Hewad Evaluate the following double integralr: Luz Lus 2x+y e dy dx Vx dxdy

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Q: 38 a Complete the square for x² – 8x + 25. b Hence find 2x +7 dr. x² - 8x + 25

A: To complete the given square and to evaluate the given integral.

Q: d²y What is the particular solution to the differential equation x dx? dy x² with y = 0 and dy = 1…

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Q: KA spherical tank with radius of 125m can hold a volume of 25m'3 Use Bisection and Regula Falsi…

A: Given that a spherical tank with radius R=12.5 m can hold a volume V of 25 m3. The volume of liquid…

Q: Find an isomorphism from the group G = to the multiplicative group {1, i, – 1, – i} in Example 3 of…

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Q: Find the laplace of each f(t) (e3t+e) sin2t 4. 2e7t

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Q: Consider the matrix (, (a) Find the eigenvalues of A. (b) Find two eigenvectors v and w of A with…

A: Note : " As per our guidelines we will solve only three subparts . If you want any specific subpart…

Q: Solve the given system of linear equations using the Elimination Method. 4.)     2x1 + 7x2 + 15x3 =…

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Q: You want to receive ​$400 at the end of every six months for 5 years. Interest is 11.8% compounded…

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Q: exercise Find the laplace of each f(t) 2. sin8t sin6t

A: We have to find the Laplace transform of ft=sin8tsin6t

Q: Let! aset os R, sho that whe ther Tbe acofinite to pology on (R,T) is To-spuce and TisPuceand or not…

A: The given question is related with topology. Given that Τ is the co-finite topology on R . We have…

Q: Determine if the set S is span set of %3D R2x2. Solution:

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Q: 86s - 78 Find the Inverse Laplace Transform of +3)(s-4)(5s– 1) - 2e -+ 3e+e3 В 41 - 3e

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Q: What is the general solution to the differential equation y- (9 - + = 0 ? dx In(Ay – 2) = Ax +B y2 =…

A: We have given a differential equation ,  yd2ydx2 - dydx2 + dydx = 0 This can be written as ,  y y''…

Q: What is the interquartile range of the data set below? 3, 5, 6, 6, 7, 8, 9

A: Interquartile range is given by : Q3 - Q1

Q: Calculate the curvature and radius of curvature of the graph of the function y = xe

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Q: Evaluate the integral shown using Simpson's 3/8 Rule with 9 panels. 12 4arctan () dx O 32.52020854 O…

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Q: dan Elimination. 1. x1 + x2 - x3 = -2 2x1 - x2 + x3 = -5 -x1 + 2x2 -3x3 = -

A: We solve this system of equations using gauss jordon elimination .

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

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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: rm of the wayeform

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Q: Find the solution. xy'+ xy = 1 - y, y(1) = 0 A y = x-'(1 – e!-") y = x-2(1 + e'+*) © x=y-'(1 + e'-1)…

A: Given differential equation is xy'+xy = 1-y, y(1) = 0

Q: [2 - 3 2 - 3 and be express as A = LU as below 14 – 1 – 2 1 * c) Let A = |1 1 01 [411 U12 U13 [2 - 3…

A: The solution is given as

Q: Use Laplace transforms to solve the initial-value problem. x'' + 4x = cos t;   x(0)=0, x'(0)=0

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Q: Integrate f(x) from x = 0 to 10 using Three-Point Gauss-Legendre Quadrature. f(x) = 5000 + 24583x –…

A: Gauss's three-point formula to evaluate the integral I=∫abfxdx is: I=b-a2w1fx1+w2fx2+w3fx3 Here we…