1. Find the Laplace Transformation of the following function. First express the function in terms of u (t). Then use #12 from the Laplace table. g(t) 3 ,0 < t < 5; 10,5≤t≤8 0 ,t≥ 8.

Q: Evaluate the line integral, where C is the given curve. [x² x sin(y) ds, C is the line segment from…

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A: Given: Interest rate, r = 4% =4/100=0.04 Final amount, A = $500 Number of years, t = 4

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Q: 3. Find all values of in the interval [0,2r] that satisfy the given equations. Your answer(s) must…

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A: Solution is given below:

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Q: Rewrite the equation with the variables separated. -ydy + sin(x) = 6 dx dy O = [6+ sin(x)] dx ey o…

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Q: Solve the initial value problem. y' = (x − 1)(y − 6),  y(2) = 6   PLEASE SHWO STEP BY STEP .

A: Here we have to solve given differential equation

Q: Consider the following equation. f(x, y) = y³/x, P(1, 3), (a) Find the gradient of f. Vf(x, y) = u =…

A: As we know the expression for the gradient vector. ∇fx,y=i∂∂x+j∂∂yfx,y=i∂fx,y∂x+j∂fx,y∂y The given…

Q: Given: f(x) = x³ − 6x² + 9x + 5. Find the ABSOLUTE MINIMUM value of f (x) on [−1,2]. A. -11 B. 7 C.…

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Q: Use the alternative form of the dot product to find u. v. ||u|| = 50, ||v|| = 25, and the angle…

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Q: . Find the local and absolute minima and maxima for the function over (-∞, ∞). 3 y = x³ (1-x)6

A: Given, y=x31-x6

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Q: Use your parametric equations to determine the following: Maximum height Time to land Where to…

A: Disclaimer: Since you have posted the sub multiple parts for the questions ,we will solve the first…

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Q: A particle is moving with the given data. Find the position function, s(t), of the particle. [Note:…

A: Solve the following

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Q: Find the limit of the transcendental function. Ilm sin 7tx

A: topic- limits

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A: ∫0π3x sin(x)dx

Q: Find the general solution to the differential equation. (4 + x)y' = (x + 5)(y − 4) y =

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Q: Calculate the integral of ze²x+y over the surface of the box with 0 ≤ x ≤ 2,0 ≤ y ≤ 3,0 ≤ z ≤ 6.…

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Q: Give the interval where y is decreasing y=x²e^x

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Q: 17) Find the solution to the initial-value problem. dy dx = y3xex2, y(0) = 1 y =     PLEASE SHOW…

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Q: Work Problem 3 a) Find the local maximum and minimum value(s) (if it exists) of the function f(x, y)…

A: This is a problem related to maxima and minima. Please follow the procedure given below. As per…

Q: Use the method above to find a second independent solution of the equation ty" - y' + 4t³y = 0, t >…

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Q: Express the number 7√3-3i in the form R(cos(0) + i sin(0)) = Rei, where R> 0 and ≤0 ≤TT. NOTE: Round…

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Q: nd barely audible to the human ss the formula so that the expression in parentheses is written as a…

A: topic:- algebraa

Q: 3).   Draw the directional field for the differential equation. y' = 3y + xy

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Q: The population of a species of bird in an area can be modelled by the equation P(t) = 450 + 200 cos…

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Q: Find polar coordinates (r, 0) of this point with I with expressed in radians. Lets r > Oand 0≤0<2…

A: The objective is to find the polar coordinate.

Q: Find an equation of the plane with the given characteristics. The plane passes through the point…

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Q: 5 [³ (Use symbolic notation and fractions where neede Calculate the integral, assuming that f(x)dx=

A: topic:- integration

Q: Question 2 ( by the curves y = ) Draw the enclosed regio /1 1- x, y = 0 and x =

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Q: 2. Set up, but do not evaluate, the integral which gives the volume when the region bounded by the…

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Q: Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep…

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Q: In Problems 1-5, let R be the region bounded by y = 4(x - 2)² and y=x. Each problem will describe a…

A: Since you have posted multipart questions so I have solved first three subparts as per our company…

Q: Problem 3.11 Calculate the differentiation of tan(x/y) = x + 6

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Q: 4. Match each of the following differential equations with a solution from the list below. A. y =…

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Q: (f) If F(x, y) = 5y sin(xy)i + 5x sin(xy)j, f(x, y) =

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Q: Question 2 ( ) Draw the enclosed region by the curves y = √1-x, y = 0 and x = -3.

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Q: 9. Find the solution to satisfying y = dy dt = 7y || y(6)=9

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Q: Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t 2 0. Then…

A: A detailed solution is given below.

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A: We have to choose the correct options according to the given information

Q: 13 Find p, q if f f(x) dx + f₂³f(x) dx = f f(x) dx. (Give your answers as whole or exact numbers.)…

A: NOTE: Refresh your page if you can't see any equations. . use the integration rule

Q: If f(x) = 2x + 3 and g(x) = 3x + 2, what is the value of f(g(3))? 16 O 20 O 25 O 29

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Q: Suppose that f(x) and g(x) are two functions and we know that: ƒ( − 3) = 0 g( − 3) = 2 ƒ'( − 3) g'(…

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Q: (в Consider the integral f sin ¹x dx. If we let u = sin ¹x and dv=dx, the integral can be written as…

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Q: Find the shaded region in the graph. 4 3- NO 2 1 X = y=2 y = cos x + 1 π/6 E|M 3 πV3 π: ….. The area…

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Q: Expand f(x) = √3+x as a binomial series. 2 / 3 (¹ + $ 1 E 0 + (¹ + 5, (1 1 O O₁+ (-1)1-3. 5 . n=1…

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