1 1. Suppose we have the function f(x) = = and then we transform it by moving it four units to the right and six units down, reflecting it horizontally, and stretching vertically by 5 units. What will the formula of our new function g(x) be? (2 points) g(x) =

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Q: By using Laplace transforms, solve the following differential equation subjectto the given initial…

A: Used Laplace Transformation:

Q: 2) Compute the following anti-derivative. √1x4 dx

A: REFERENCE…

Q: || 8 Example: If ƒ (x + 2π) = f(x), obtain Fourier series expansion for the function given by 2x 1+…

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Q: (b) / dx - 2 +C 1. Use the Fundamental Theorem of Calculus to solve the following: (a) (x³ + 1) dx…

A: Question 1: Using the Fundamental Theorem of Calculus

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Q: Question Given the following piecewise function, evaluate lim f(x). f(x) = x+1- -2x² - 2x 3x-2 2 x²…

A: Step 1: Step 2: Step 3:The answer is 1.

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Q: use the Laplace transform to solve the initial value problem.

A: Step 1:The provided initial value problem is:y′′−y′−6y=2   .........(1)with the initial conditions:…

Q: 2. (15 pts) Write the Maclaurin series for the function f(x) = sinx. Use it to write the Maclaurin…

A: ### 1. Maclaurin Series for  f(x) = sin x :  The Maclaurin series is the Taylor series expansion of…

Q: 2) Drive the frequency responses of the following rotor system with Non-Symmetric Stator. The system…

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Q: Solve the initial value problem: y= 0.05y + 5 y(0) = 100 y(t) =

A: We are solving the initial value problem: dtdy​=0.05y+5,y(0)=100.  This is a first-order linear…

Q: (1) (4 points) Give a parametrization c: R R³ of the line through the points P = (1,0,-1) and Q =…

A: Step 1:Step 2: Step 3: Step 4:

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A: (a) Parametric Equations of the LineThe vector PQ​ is given by:PQ​=Q−P=(2−3,0−(−1),5−4)=(−1,1,1)This…

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A: Step 1: Rearrange into separable form Multiply through by 2u to separate variables:…

Q: by series find the Solution U (x) = x²- X³+ x²+'S (1+x+) u(t) st 0 (2) u(x) = x's (6x-2+) u(t) St U…

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Q: Find the value c in the interval [a, b] given by the mean value theorem for the function f(x) =…

A: Equation of the tangent line Graph

Q: Solve this differential equation: dy 0.05y(900 - y) dt y(0) = 2 y(t) =

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Q: xux +yuy =2xy,withu =2 on y = x2

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Q: 43..1 ) Can you please solve this. I am trying to do practice problems to prepare for a test but I…

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Q: Find the exact length of the curve. - x = 5 cos(t) = cos(5t), y = 5 sin(t) - sin(5t), 0 ≤ Z ≤ π

A: We find the exact length of the curve defined parametrically by x(t) and y(t) by using the formula…

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Q: Let g(x) = f(t) dt, where f is the function whose graph is shown. y 5 f 20 30 t (a) Evaluate g(x)…

A: Step 1: Step 2: Hint:- In (b) I used mid-point theorem. Step 3: Step 4:

Q: • -7 10 1.0 (2 - x) for 0 < x < 2, Let f(x) = for 2< x < 6. Compute the Fourier cosine coefficients…

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Q: • • Let > be a potential for the vector field F = (−2 y³, −6 xy² − 4 z³, −12 yz² + 4 2). Then the…

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Q: Proof that: d (sechu)= dx show that: coth x = 1/2 m² (x+1), du и Пит dx -(054≤1) 1871 X711 X-1 Proof…

A: Step 1: Step 2: Step 3: Step 4:

Q: find a simple formula fot the nth term of the following sequences 1, -2, 3, -4, 5, -6, ...

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Q: A line (L1) is perpendicular on the line (L2: 5X - BY +19-0) and intercept it at a point (-5, 2).…

A: Approach to solving the question:  Find the value of B such that L1 (a line passing through (−5,2)…

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Q: 10. Consider the polar equation r = sin² (2) a) Find the (rectangular) equation of the tangent line…

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Q: find three soultion independed by lagrang 2x (y + z²)p + y(2y + z²)q = Z³

A: Let's give it a try. To provide precise answer, I believe further reference is necessary, but I will…

Q: Solve: coshx-1.dx do Sinho + cosho Solve: S Salve dx 4-x2 Solve dx √ex+1 If y = (x² +1). sech (lax),…

A: Step 1:  Step 2: Step 3: Step 4:

Q: Hi I really need help with how to answer question 3 in attached image, the one that asked the…

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Q: Please help on all asked questions. Please show all work and steps. Please circle the final answer.

A: i) The planes are coincident:For planes to be coincident, they must be scalar multiples of each…

Q: Find the radius of convergence, R, of the series. Σ n!(9x – 1)" n = 1 - R = Find the interval, I, of…

A: To determine the radius of convergence  R  of the series∑n=1∞​n!(9x−1)n,we can use the **Ratio…

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A: Thus area of parallelogram is same as finding the magnitude of cross product of the two vectors.

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Q: Example: If ƒ (x + 2π) = ƒ (x), find the Fourier expansion f(x) = eax in the interval [−π,π]

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Q: "l Use implicit differentiation to find Əz and az ах 2 22 ay 3 x ² 2 - x², ² + 22² = 3 y 2 - 5=0…

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Q: Please help me with these questions. I am not understanding what to do. Thank you

A: 1. 2.Explanation:

Q: 36. Target Weight. The target weight w for an adult man of medium build is w(h) = 0.0728h² - 6.986h…

A: Step 1: Step 2: Step 3: Step 4:

Q: 7. Let F(x1, x2) (F₁(x1, x2), F2(x1, x2)), where = X2 F1(x1, x2) X1 F2(x1, x2) x+x (i) Using the…

A: Solution:  (i) Calculate the line integral ∫γ​F⋅dγ The given vector field is:…