1. Write the following function using unit step functions and then find its Laplace transform: 0 2. f(t) = { (t - 1)²,

Q: Consider the real sequence {an} given by an = ln(n + 1) − ln(n + 2), n ∈ Z≥0 = N ∪ {0}. Justify…

A: Given series is telescoping series  An infinite series to be convergent if its limit of the partial…

Q: 3. Consider the following formula f(x) = lim n-0 gn +1 Let D = {r E R : f(x) E R}. Calculate f(r)…

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Q: Solve the following differential equation Integrating Factor by Linear Equations: dx/dy + xcoty =…

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Q: Let n = pq where and q are two distinct primes and consider Z,. Further, let [a] E Z, be an…

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Q: (D + D,)'u=0 %3D

A: We have to solve given problem:

Q: Completed this t:able of percemtage nterest rates. Annual rate Sbr monthly rate Quarterly rate…

A: To complete the given table :-

Q: Let F(s) be the Laplace transform of f(t). Find the Laplace transforms of the following expressions…

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Q: Prove that l17 is the only prime number of the form n²- 64.|

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Q: 5x sec Suppose m' is continuous at r = 0 and m'(x) if x > 0. log3 (2.x + 1) + cosh r If m" (0) = 0,…

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Q: Q4/ Solve the differential equation dy b) = V1 + sinx(1+ y?) when y(0)=1 dx

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Q: Solve the following problem over the interval from x = 0 to 1using a step size of 0.25 where y(0) =…

A: Given differential equation is dydt=(1+4t)y      (1) with initial condition y(0)=1 and t varies from…

Q: distance between point Al2,4) Perpendicular on the line L:3y=3+X is solution:- 1) 149.3 2) 53,41 3)…

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Q: PLEASE ANSWER ALL QUESTIONS Consider the vector space V = C² with scalar multiplication over the…

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Q: H.w: Find LT-' of the following functions: 1- L-1 s2-2s+2]

A: Dear Bartleby student, according to our guidelines we can answer only three subparts, or first…

Q: Solve the initial value problem (3+x²)y" + 4y = 0, y(0) = 0, y (0) = 12. If the solution is y = co +…

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Q: 10 f(x) = g(x): for a x+1 nction g?

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Q: F = [r. -x, 0]. = [y. -X, S: 3r + 2y + := 6, x2 0, v 2 0, z 2 0

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Q: Find the number of distinct regular tetrahedral dice that can be made by coloring its faces with…

A: The fundamental theorem of finite Abelian groups - " a finite Abelian group is isomorphic to a…

Q: Consider the graph as shown in figure and determine the following: Pendant vertices, pendant edges,…

A: 1. Pendant vertices are d,e,f,g Pendant edges are ad edge,eb edge,fb edge,gb edge, Odd vertices are…

Q: Suppose that f e C(R) and that | If(x)|dx converges. Show then that 2 f(x)| sin nx|dx sx)dx. lim n00

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Q: At 12:00 p.m. a tank contains 150 g of salt dissolved in 8 L of water. Pure water begins flowing…

A: Since you have asked multiple questions, we will solve the first one for you. If you want any…

Q: dx CoSX dy= 3 GoSX dx ( 3x+2) dy Six

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Q: Use Eq. (1) to prove the recurrence relation: (n + 1) Pr+1 = x(2n + 1) P – n Pn-1

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Q: Find the inverse to 2 by using the Euclid's algorithm  2 mod

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Q: What is the square root of -5?

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Q: Solve the system using either of the three direct methods 1. x - 2y + 2z = 3 2x – 3y – z= -7 -z + 3y…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: find general and particular solution of differential equation y" + 2y' + 5y = 0 with the given that…

A: Solution:-

Q: Prove that l17 is the only prime number of the form n²- 64.

A: We have to prove that 17 is only prime number of the form n2−64. Since, n2−64=n+8n−8 Let for some…

Q: b- Using the variation of parameters, find the general solution of the second order differential…

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Q: 1) Find all integral solutions of the linear Diophantine equations 6x + 11y = 41

A: Solution:- As per guidelines I submit first question only

Q: 2. a – 2y + z = -6 2x – 3y –- z = 11 -x + 4y – 3z = 28

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Q: 7. What is the eighth term of the geometric sequence the 3rd and 6th terms of which are 5/4 and 10,…

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Q: The value of a certain photocopying machine t years after it was purchased is defined by P(t) =…

A: Given that the value of photocopy machine after t years from purchase Pt=ie−0.25t And after 6 years…

Q: 2. Find the Fourier series expansion of: So, -1550 f(x) = sin nr, 0<r< 1 and then use it to find the…

A: Solution :-

Q: Let V=R? Prove that V is not a vector space over R with respect to the following standard addition…

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Q: 3. Let L: R4 → R³ be the following linear transformation: 2x + y – w + 4z -x + 4y + 5w + 2z x – 3y +…

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Q: The number of bacteria B(t) in a petri dish culture after t hours is given by B(t) = 400e0.876t When…

A: Given that The number of bacteria B(t) in a petri dish culture after t hours is given  To find When…

Q: 4. Let B = {v1, v2, v3} and C = {w1, w2, w3} be bases for R3, with vectors defined below. -(:) --()…

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Q: 3. Let X= {a,b,c} with and r, = {ø, X,{a,b},{b},{b,c}} and Y ={1,2,3} with topology T, =…

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Q: 7) Find the centroid of the region in the first quadrant bounded by the x-axis, the parabola y = 2x,…

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Q: Hello. According to the question's correct answer from the multiple choice, it's 2 3/4. However the…

A: According to the question's correct answer from the multiple choice, it's 2 3/4. However the expert…

Q: GRAD, DIV, CURL, V, DIRECTIONAL DERIVATIVE Let f = zy + yx, v = [y, z, 4. - x], w = [y, z?, x2].…

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Q: Prove that an angle of θ radians is constructible if and only if the real number cosθ(sinθ)…

A: Since θ is constructible, by definition, (cosθ, sinθ) is a constructible point.

Q: 1. a) Find a linear transformation L : R³ → R³ whose kernel is spanned by the set {{:) (}} S = 6)…

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Q: Solve the following differential equation Integrating Factor by Linear Equations: dy/dx = 1/x+y2

A: We have given a differential equation, dydx = 1x + y2 ⇒ dxdy = x + y21 = x + y2 ⇒ dxdy = x + y2 ⇒…

Q: 9. Solve the given (matrix) linear system: [1 0 X' = 1 5 L2 4 -3] 1 X %3D

A: Solution :-

Q: 4.1.3. (-) Let G be an n-vertex simple graph other than Kn. Prove that if G is not k-connected, then…

A: Given: Let G be an n-vertex simple graph other than Kn. Prove that if G is not k-connected, then G…

Q: Let Gbe an open set in R". Two points x, Y e G are said to be equivalent if they can be joined by a…

A: Since every open subset of Rn can be written of countable union of disjoint open balls and each ball…

Q: in 2013, countries U and O have a population of about 20.5 million. However, it was recently…

A: Given that in 2013, countries U and O have a population of about P0=20.5 million.

Q: ploy Crout's decomposition to solve the system. 5x1 – x2 = 9 -x1 +5x2 – x3 = 4 -x2 + 5x3 = -6

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