Use appropriate algebra and Inverse Transform Theorem to find the given inverse Laplace transform. 1.4-¹ {3} 2. 4-1 {(275) (2+1)}

Q: 1. Use the definition (e-6) of the limit to show that lim f(r. y) does not exist for (z,y)-(0,0)…

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Q: (a) Let (an) be an increasing sequence of real numbers bounded from above and (bn) be a decreasing…

A: (a)  (i) Take  an=tan-1n  and  bn=-n  . Then       {an} is an increasing sequence of real numbers…

Q: Evaluate the surface integral , 2zds; o is the part of the following tetrahedron bounded by the…

A: We have to evaluate the surface integral ∬σ2zds where, σ is the part of the given tetrahedron…

Q: , Let p be an odd prime. Prove or disprove the following statements. (a) If p = 2 + 1, then every…

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Q: 5. Consider the function defined by f(x) = e²-¹. a. Determine the Taylor series expansion of f at x…

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Q: Find the value of P = 11 n=1 stn²()]if it exists. 2+ sin

A: Solution :-

Q: 2. The rectangular similar What are the values of x and y? prism prisms shown below are 12 in

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Q: 6. A two-story building measures 21 feet from the ground. A scale model shows the building to be 3…

A: Let be "x" the height inches (in the model) of a 84 foot building. Given that the height of a…

Q: 7. Find the area of the region enclosed by the curves y=x²-2 and x = y.

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Q: From Example 10.1.1, obtain the solution when f(x) = 2x.

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Q: 5. Find the area of the surface formed by revolving the graph of y= 8 about the x-axis √x + 2 from x…

A: Given: y=x3+2, x=1, x=8 We have to find an area of the surface of revolving about y-axis.

Q: Let {u₁(x) = −9, u₂(x) = − 12x, uz (x) = − 12x²} be a basis for a subspace of P₂. Use the Gram-…

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Q: Find дz ?x дz and on the surface ду (-3x + z)3 - 7x5 . y6+9y.z6+11y4. z = 21 in terms of x, y and z.

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Q: Use the tangent line to the curve x² + y² = x + y at the point (1, 1) to approximate the…

A: Given information Curve: x7+y2=x+y Point: 1,1 Approximate the y-coordinate of a point on this curve…

Q: 2. Determine an equation for a cosine function that has a period of 1800°, an amplitude of 3, a…

A: Given that Period =1800°amplitude=3vertical shift =4 phase shift =225°

Q: Kari is purchasing a home for $260,000. The down payment is 25% and the balance will be financed…

A: The answer provided below has been developed in a clear step by step manner.

Q: Prove that _f₁ = = ₁+2 +851+1 −85₁-1 + ₁-2 +0(hª) 12h

A: Use taylor series expansion to prove this

Q: Using the RREF Solution: V₁ = (1, 3, 5) V₂ = (2, 1,5) V3 = (3, 4, 10) Augment the given vectors to…

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Q: (a) Prove that is continuous on [−1, 1].

A: The given series is h(x)=∑n=1∞xnn2. To Prove: This function h is continuous on -1,1.

Q: Row reduce the matrices in Exercises 3 and 4 to reduced echelon matrix and in the form. Circle the…

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Q: 1-2- Find DCM for the following Euler angles using MATLAB: a- Rotation about the Z axis (Yaw angle -…

A: The direction cosine matrix (DCM) is a matrix that describes the orientation of a coordinate frame…

Q: Transform of a Derivative Theorem 3. y" +9yet, y(0) = 0, y'(0) = 0 4. se {telor} L S 5. 4-1 { 1 +…

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Q: te Given a connected graph G, define the diameter diam(G). Calculate diam (C5), i.e. find the…

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Q: 3 The matrix A = 8 11 eigenvalue > A. λ = -14 Β. λ = 3 C. λ = 14 D. λ = -3 E. None of them. 0 001 6…

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Q: 4. The series given by Σ( √5 - (-1²) is n n=1 (convergent/divergent)

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Q: Calculate limits and explain why they converge or diverge, state what theorem you will use. i. limx…

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Q: A bag contains​ pennies, nickels,​ dimes, and quarters. There are 50 coins in all. Of the​ coins,10​…

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Q: Stokes’ Theorem for evaluating surface integrals Evaluate the line integral in Stokes’ Theorem to…

A: Given: F=y , 1 , z and S is the part of the surface z=2x within the cone  z=x2+y2. To Find…

Q: huck Wells is planning to buy a Winnebago motor home. The listed price is $145,000. Chuck can get a…

A: The answer provided below has been developed in a clear step by step manner.

Q: reflected over the x-axis, then translated 6 units left

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Q: Use a CAS to perform the following steps for the sequences a. Calculate and then plot the first 25…

A: The given sequence is: an=nsin1n. To Do: (a) Calculate and plot the first 25 terms of the given…

Q: a. Find the Euclidean distance between u → and v and the cosine of the angle between those vectors.…

A: As per our guideline, part a solved. Please repost the other questions as separate question.

Q: 2. Find a Fourier series particular solution for nonhomogeneous vibration equation where the…

A: Given,               d2udt2+u=F(t), where the periodic driving force F(t), and the graph is given…

Q: Use the chain rule to find the derivative of 8√7x³ +5x6

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Q: 3. Please work out the solution for x(t). (Hint: Assume x(t) = cet) (3) Find x + 4x(t) + 4x(t) = 0.…

A: (3) x¨t+4x˙t+4xt=0 Therefore the characteristic equation of the second order homogeneous…

Q: For the situation, classify each item as an undefined term, a defined term, a postulate, or a…

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Q: (e) Let another probabilty density fx,y be given by Sce-(√²+√)²+2√y Fx.x (2, 1) = { ce if x ≥ y ≥0…

A: In probability theory a probability density function, or in other words density of a continuous…

Q: What are the Karush–Kuhn–Tucker conditions and what are they related to? b. Maximize function…

A: (a) Karush-Kuhn-Tucker Condition: For a convex non linear optimization problem, Karush Kuhn tucker…

Q: Consider the system of equations shown below. 3w 2x + 16y - 2z = -9 -W + 5x 14y + 18z = 23 3wx+14y +…

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Q: Prove using induction, for all real x>-1 and n a positive integer

A: (1+x)n≥1+nxto prove by mathematical induction

Q: Hint: For this question you may find it helpful to remember that a2-62(a+b). (a−b). = For subject to…

A: The given function Fx, y=4xy-24x+y subject to the constraints x2+y2=36. We have to find the maximum…

Q: Find the stationary point of on the plane F(x, y, z) = x²y³ 4 3 and the value of F at that point. b…

A: Given: find stationary point of   F(x,y,z) = x4 . y3 . z2   ....(1)   On the plane   5x + 4y - 2z =…

Q: Find the equilibrium quantity and equilibrium price for the commodity whose supply and demand…

A: We are given demand and supply function of a commodity. We have to find the equilibrium quantity and…

Q: For the iterated integral ſˇª ſ y √4-y² px² + y² √(x² + y²)² + 9, dz, dx, dy 10 (A) sketch the…

A: The given integration is ∫02∫y4-y2∫0x2+y2x2+y22+9 dz dx dy. (A) Sketch the region in cartesian…

Q: 57 a +25³ +35² + 4s+5 = 0 4 95 an as ar 7

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Q: 9(x) = ² + (x-1)e-x)(1) dt. 0

A: Here we need to find the solution of the given integral equation using Laplace transform. To find…

Q: (a) Solve the following inhomogeneous wave equation on the real line Utt-c²Urr = 2x - sin r U(x, 0)…

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Q: 3. The triangular prisms shown below are similar. What are the values of x and y? 8 cm 20 cm X 4 cm…

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Q: Question 20 Let V be a vector space and suppose T: V→ V is a linear map satisfying T2 = T. Prove…

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Q: Starting with the graph of f(x) = 4x, find a formula for the function that results from: Shifting 4…

A: The given function is fx=4x. If the function fx is shifted a units upwards then the formula of the…