Find the Laplace transform of the following functions. (a) S6 0 < t ≤ 3 = 2 t≥ 3 {{ f(t)

Q: Solve the following initial value problem using (Laplace Transform) 9y''-12y'+4y=x4 y(0)=2…

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Q: 68. π/2 0 cos x sin (sin x) dx

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Q: Let's consider the marginal cost function C'(x) = - where a represents the level of production and…

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Q: Find all values of t in the interval [0, 2π] satisfying the given equation. (Enter your answers as a…

A: The given equation is: 15tant-15=0 ; 0,2π

Q: Given z = ² and y - sinh (21) where t > 0. Find and d'y dr² in terms of z.

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Q: Is the following series convergent or divergent? 1 Σ Inn n=2

A: Given data, ∑n=2∞1lnn

Q: Find f f(x, y) dA where f(x, y) = x and R= [5,8] × [-3,2]. SSR f(x,y) dA= Preview My Answers Submit…

A: The rectangular region is R=[5,8]×-3,2. So, 5≤x≤8 , -3≤y≤2. Also, fx,y=x. So, the double integral is…

Q: (1,3,-5)

A: Let a=1,3,-5

Q: O t = 2.1 t = 3.4 O t = 3.9 O t = 1.2 6 5 4 3 2 1 0 2 Velocity vs Time 5 The velocity of a particle…

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Q: Calculate the integral approximation Se for S6 = 8. 1₁4² dz.

A: Given:    ∫-104-x2dx Simpson's rule S6:   ∫abf(X)dx=∆x3fx0+4fx1+2fx2+... where ∆x=b-an,       a=-1,…

Q: 35. F(x) = x4/5(x − 4)² 37. f(0) = 2 cos 0 + sin²0

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Q: Calculate the definite integral by referring to the figure with the indicated areas. Area A = 1.574…

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Q: 5. Find the values of a and b such that f(x) is differentiable everywhere sin x T sin x - cos x 2…

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Q: Find the value of y for the given differential equation if the value of the arbitrary constants is…

A: The given differential equation is: y''-2y'+1=(x+1)e2x

Q: 41-54 Find the absolute maximum and absolute minimum values of f on the given interval. 41. f(x) =…

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Q: Evaluate [*(z + √1 − 2²)da by interpreting in terms of areas.

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Q: What is the antiderivative of dx/((1+x^2)^2)?

A: We have to find the antiderivative.

Q: 7. Assume What is t 60 X=S X y y is the Area? + E.ON

A: We need to find area.

Q: Let f(x) = 4√√x+5x. Verify that f(x) satisfies the conditions of Mean Value Theorem on the interval…

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Q: 1. The coefficient of x³y³ in the expansion of (2x + 2y)¹⁰ is 20 2. The constant term in the…

A: Question 1,Given,            2x+2y10To find : The coefficient of x5y5 in the given expansion.We know…

Q: 4) 1z In 4

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Q: Assume that and y are both differentiable functions of t and are related by the equation 7- cos (62)…

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Q: Evaluate the indefinite integral. Use a capital "C" for any constant term. 3 /(-28/8) dz = [ dx x5/3…

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Q: Find the absolute max and min for f(x,y) = 2x2 + 3y2 on the set {x2 + y2 <= 1}

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Q: Solve the equation algebraically, and then use a calculator to find the values on th [0,2π).

A: Given query is to find the solution of the expression.

Q: What form of the particular solution is appropriate for the differential equationy"- y'=4? (A) y =…

A: Solution: Given differential equation is, y"-y'=4

Q: S sin 3x (csc 3x - cos ³3x) dx

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Q: Find an equation of the hyperbola that has vertices (0,±6) and foci (0, ±7). Equation: 1

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Q: Determine the values of where the function f (x) is not continuous. Label each discontinuity as…

A: Given Functionfx = x3+5x≤3x+3x&gt;3

Q: For f(x, y) = e²z+15y, find the second order partial derivatives fry and fyr of the function. O…

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Q: Suppose f'(x) = 8x³ + 12x + 2 and ƒ(1) = −4. Then f(−1) equals . (Enter a number for your answer.)

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Q: 2. Sketch the graph of a function that satisfies all of the given conditions. • f'(-2)=f(0) =…

A: The graph of the function satisfies the condition, f'-2=f'0=f'2=0 f'x&lt;0 if x&lt;-2 or…

Q: Find a positive angle and a negative angle that are coterminal with the given angle. Answers may…

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Q: Calculate the definite integral by referring to the figure with the indicated areas. Area A = 1.261…

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Q: 1. Consider the sequence a₁ = cos² a. Does the sequence converge, or not? If it is convergent, find…

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Q: У 2- -2- П 2л X

A: Graph of the function is given, we have to find its equation.

Q: 43-44 Evaluate the integral and interpret it as the area of a region. Sketch the region. T/2 ³. √5¹²…

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Q: Problem 5: Find the two points on the curve y = 2x² that are closest to the origin. (Explain why x =…

A: NOTE: Refresh your page if you can't see any equations. . as we can see the given function is a…

Q: Determine the convergence or the divergence of the series: 8 W [2inn n=1

A: Given data, ∑n=1∞2lnn

Q: Imagine a spherical balloon filled with gas whose volume V is increasing at a constant rate of 3…

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Q: The distance, in feet, a stone drops in t seconds is given by d(t) = 16t2. The depth of a hole is to…

A: Given: d(t)= 16t2 dt= 2/10th of a second

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. S - f³ ct…

A: The given function gs=∫7st-t43dt. We have to find derivative of gs, using Fundamental theorem of…

Q: How do I find a and b?

A: We will find the required.

Q: Find the volume generated when the region defined by y = x, y = 2x/(1 + x3) is revolved around the y…

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Q: Determine convergence or divergence of TL A. converges B. diverges Vn 7n +8

A: The objective of the question is determine the converge or diverge of the series and choose the…

Q: If a firm has the following cost and revenue functions, find the break-even points. + 1/2 x ²…

A: NOTE: Refresh your page if you can't see any equations. . given the cost and revenue functions are

Q: Determine a suitable form of a particular solution if the method of undetermined coefficients is to…

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Q: Approximate the derivative of the function f(x) = sin (x²) on the interval [0, 2] in steps 0.25…

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Q: y"y"+16y' - 16y = 0

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Q: Evaluate the following double integral over the region R by converting it to an iterated integral.…

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