The value of the limit lim a) 0 b) 1 c) d) ∞ 1 X x-0 sin x sin x 6 is

Q: 2. Which of the following is NOT a path in the graph? B E FO OA) FEBA OB) FBCCD OC) FEABCD OD) All…

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Q: Let (G, 0) be a group and x € G. Suppose H is a subgroup of G that contains x. Which of the…

A: The detailed solution is given in the next step. The solution is based on properties of subgroups.

Q: Find the Fourier Series of the given f(x), in which the periodicity is 27 f(x) 0 if -≤x<0 sin x if…

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Q: 1. Which of the following is NOT a circuit in the graph? E FO OA) CBEC OB) ABEA 0 C) BCDCB Figure 1…

A: Vertex is where two or more edges meet. The circuit is a path in a connected graph in which the…

Q: Choose any that is an arithmetic series. 4+8+12+16+...+200 50 Σ(1-2) j=5 45 Σ(12 + 3) j=1 45 Σ 3* K…

A: Here we have to choose the arithmetic series. A series is said to be arithmetic series if difference…

Q: t, +) = { (+ (t-7)², (11t - ²1-ar g(t) 4St<7 t27

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Q: Give an explicit example of each of the following: (a) Two power series f and g in the complex…

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Q: Consider the following table. Xį 4.0 4.2 4.5 4.7 5.1 5.5 5.9 6.3 256.73 Y₁ 102.56 113.18 130.1178…

A: The table given is as follows: x 4.0 4.2 4.5 4.7 5.1 5.5 5.9 6.3 y 102.56 113.18 130.1178…

Q: 8. Given av av 25202v ат +S as² as find a change of variable of S to x(S) so that this equation has…

A: Solution: Given ∂V∂τ=2S2∂2V∂S2+S∂V∂S-V given condition is a change of variable of S to x(S), So our…

Q: 1. Determine the linear convolution of the finite length sequences below using Graphical Method.…

A: Solution : y(n)=∑k=-∞∞x(k)h(n-k) x(n)={3,-1,4}h(n)={2,1,4} plot first x(n) first, then plot h(n),…

Q: The following are pen-tracing puzzles. For each shape, can you find a way to trace the shape without…

A: The Eulerian path for a connected graph is the path along which each of the graph's edges can be…

Q: 3. Transform the following to Laplace equivalent a. y(t) = of усь +0 5 -66 3 b⋅ y ≤t) = 100+ € ² +…

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Q: Š The minimum value of n required to approximate dx by composite Simpson's Rule with an error less…

A: Given integral is ∫02e−2xdx. We have to find the minimum value of n required to approximate…

Q: 1. f(t) = 5t²u, (t) + 3(t-4)³ un(t)-9 sin()us(t)

A: This is a problem of Laplace Transformation.

Q: y² = x x-1

A: We have to sketch the following curves.

Q: Answer the following and show solutions Given the following systems, 4x1 + 2x2 - x3 = 10 x1 + 3x2 -…

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Q: Let F subseteq K be a field extension and let L be the algebraic closure of F in K. Then L is…

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Q: 16. Cauchy-Schwarz Inequality for Integrals: Let f. g ER[a, b]. Prove that | [*P(Abs(x) dx] * = (…

A: Let , f , g ∈ Ra , b We need to prove Cauchy - Schwarz Inequality for integrals ,  ∫abf(x) g(x)dx 2…

Q: If the function u = ln (2¹+2²4-7² I-Y O2e^u O e^2u 0 2 O 1/2 O Other: then x + y sy Sx is

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Q: create 2 sample word problems of antidifferentiation with solutions

A: First problem: The rate of water out of a faucet is rt=t3, where t is the number of minutes from the…

Q: 3. Solve the difference equation by using Z-transform In+1 = 2n = 1+ndn, (k > 0) with = 0, where is…

A: Introduction: The Z-remodel is extraordinarily essential in conversation and manage engineering,…

Q: 1 Let ƒ(x)=x²e³² the value of — lim[ƒ(x)]¹* is: 1 a) b) c) 0 d) 1 e 1 -19 4e

A: First put value of f(x) in given limit then find the limit as in next step.

Q: Transform back to time base using inverse Laplace TU - 5s + 2 e 4⁹ X(s) = + s³ + 4s² + 4s + 1 3 s² +…

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Q: Calculate the following. Σ=30: i=30 3 + 4i I. 1 II. + …+ 1 512 16 LIT + 1 4 118 +

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Q: Find the Laplace transform of the following: 1. f(t) = 5t²u,(t) + 3(t – 4)³u8(t) — 9 sin ( - ) u₁(t)…

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Q: Create a graph of a function which satisfies all of the given conditions. • D = {x € R|x -2} R = {y…

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Q: y"" + 2y" - 11y' - 12y = 11t-9, y(0) = 0, y' (0) = 0, y" (0) = -3

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Q: 9. The number of vertices in K25 is OA) 24 OB) 25 OC) 276 OD) 300

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Q: Below are two sets of real numbers. Exactly one of these sets is a ring, with the usual addition and…

A: Introduction: Ring theory is the study of rings in algebra, which are algebraic structures in which…

Q: 17-18. cos30°sin45° + sin30°tan30°

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Q: y" - y² - 6y = t²e³t — 4t², y(0) = 0, y'(0) = −1

A: Given the differential equation y''-y'-6y=t2e3t-4t2 with the initial conditions y(0) = 0, y'(0) = -1…

Q: 3. Let V be a vector space over C and let L: V→ V be a linear transformation. (a) Give the eigenval…

A: Introduction: An eigenvector or function vector of a linear transformation is a nonzero vector that…

Q: H.W (2) Find Laplace Transform for 1-f(t) = 2t³; 2-f(t)=3e-²¹. 4-f(t)=2 cos(3t). 3–f(t)=sinh(2t);…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: f(x) = sin (√x) - x

A: Solution : Fixed point iteration, f(x)=sin(x)-x Taking  a=-0.5b=0.5 f(a)&lt;0  and  f(b)&gt;0 Means…

Q: Find the Laplace transform of the following: t, 1. g(t): (t - 4)², (9t - e20-4t t<3 3 ≤t<5 t≥ 5

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Q: A manufacturer is planning to sell a total of 500 machines to both foreign and domestic firms. The…

A: As per the question we are given a optimization (maximizing) problem, where we have to find the…

Q: 12. Find the solution u(x, t) of the wave equation Uxx = Utt on RX (0,00) such that u(x,0) = x² and…

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Q: a) Evaluate the Riemann sum for f(x) = x³ + x² - 6x +2, taking the sample points to be right…

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Q: Convert each pair of rectangular coordinates to polar coordinates where r> 0 and 0 ≤ 0 < 2π.…

A: To convert each pair of rectangular coordinates to polar coordinates where r&gt;0.

Q: C Show that dim 9 (√2, 3²/3) = Q(

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Q: Question 2 Difference equations, Laplace transforms and the Calculus of Variations. a) Suppose we…

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Q: 1. We are revising the catalogue of modules for a programme, so that each student should choose 4…

A: Given: Each student should choose 4 modules. Any choice of 4 different modules is allowed. There…

Q: a) Solve the following Initial value problem by using Laplace transforms: y" - 2y' + y = e¹²t; y(0)…

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Q: Consider (a) Find a corresponding cylindrical coordinates. (b) Find a corresponding spherical…

A: The cartesian coordinates (x, y, z) and the cylindrical coordinates r,θ,z are related as…

Q: The Laplace Transform of the figure below is in the form as shown. Find - b. Answer must be an…

A: This is a problem of Laplace transform.

Q: Solve the problem Utt = 36uTz u(0, t) = u(1, t) = 0 u(x,0) = 4 sin(2x), PDE: BC: IC: u(x, t) = =…

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Q: Determine the value of k for which Assume that k is a positive number. k 4 k 2k | = 0

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Q: Find the Laplace transform of the following: 1. g(t) = = t, (t - 4)², (9t - e 20-4t t < 3 3 ≤t<5 t≥…

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Q: Evaluate the multiple integral ay d.A where D is the region in the first quadrant bounded by the…

A: We want to find the form of given integral

Q: 4. Find the solution for the following y""+y"+ 2y = 3 y(0)= 1, y(0)=1,y)=1

A: Solution :-