Find the velocity and position vectors of a particle, given its acceleration and initial conditions as follows. a(t) = (6t, 0, –9 sin 3t) initial velocity: v(0) = (0, 2, 1) initial position: 7(0) = (3,0, 4)

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A: We are given that f:ℝ→ℝ, which follows: fx+y-2fx-y+fx-2fy=y-2 for all x,y∈ℝ.  

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Q: sin e cos e Choose the best answer: sin (0 - 1)

A: Trigonometry 

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Q: Q.3\ The Maclaurin series for cos(2x) for every x is :

A: The Maclaurin series for cos(2x) for every x.

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A: Note: - Since you have asked multiple questions, we will solve the first question for you. If you wa...

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Q: 1. lim(10 – 3x + 4x²) = ズ→4

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Q: Example 52. x log x dx.

A: ∫ xlogxdx ∫f(x)g(x)dx = f(x)∫ g(x)dx - ∫ (f'(x))∫ g(x)dx)dx   ∫ xlogxdx =∫ (logx)(x)dx              ...

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A: Topic:- application of derivatives

Q: 4 · t2k 4.t 7k k=0

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Q: Find the exact length of the curve. v= In(1 – x²). y 0 <x < 1 In(|3|) - 8.

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Find the radius of convergence and the interval of convergence. 00 Σ k(k + 1) k=1

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Q: y' +y = -x®y5 will be transformed to the following 8.

A: Given: - The Bernoulli's equation is, y'+3xy=-x8y5 To transformed: - The given Bernoulli's equation ...

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Q: C., Given the graph of the function f(x) below. Determine the value of the following for each value ...

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Q: Simplify to the form x + iy: (1 + i*sqrt(3))^13

A: Simplify to the form x + iy (1 + i3)^13 (1 + i3)2 = 1+23i-3 = -2 + 23i (1 + i3)3 = -2 -6 = -8 (1 + i...

Q: 1. Find the work done by the force F(x, y, z) = (xz, z² – x, y ), along C, the curve defined by x = ...

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Q: QI: Draw the projections of the points: A (8, 3), B (-5, 4.5), C(0,-3). D (6, -3), E (-5.5, -1), F (...

A: Solution is given below:

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A: we have of cheek and find answer

Q: cos4x - sin4x = cos 2 x 2 cos 2 x -cos 2 x

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Q: What is the derivative of f(x) = e&x + 3? a. f(x) = 8e b. f(x) = e8 C. f(x) = 8e8x+3 d. f(x) = 3e&x ...

A: We find derivative of given function.

Q: - Apply the eigenvalue method to find the general solution of the given system. Find also the corres...

A: Find your answer below 

Q: 87 1

A: Given query is to simplify the expression.

Q: 2п +1 Е. У Зп +2 n=0

A: ∑n=0∞2n+13n+2    Thus,  an=2n+13n+2    Thus, we can proceed further with ratio test

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A: Given: Newton's Law of Cooling: u(t) = T+(u0-T)ekt Where u(t): Temperature after time t T: Temperatu...

Q: The function has a relative maximum of 16 at x=| 46 (Use a comma to separate answers as needed.) 42 ...

A: Here we see that critical points of f(x) is -2,0,2  

Q: 11. Let f(x,y)=x²y+y?cosx, find Vf. einiog O lo 03002 oldizaog Ics

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A: We will find the rate of change of volume of sphere at a given radius. 

Q: In this question we use partial fractions to evaluate sec 0 de . First, write this integral as cos 0...

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A: Given : x(t)=2ln(t)y(t)=2sin(-5t)   To find : d2ydx2

Q: f(x) 1 and g(x) = 2x 1 and h(x) = 1 4x-1 flglh(x)]] = -3 1 3 1 3

A: Use function property

Q: 1 dx -1 2x+3 a.

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Q: Solve the following equation by the quadratic formula. x2 + 3x - 1= 0 3+V13 X= 2 -3+V5 X= 2 3+v5 2 -...

A: For a quadratic equation:                                     ax2+bx+c=0 The solution is of this qua...

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A: We know that, -1 ≤ sinx ≤ 1 for all real x  

Q: What is the reversed order of integration of dydx O a. 9 x²e®dxdy Ob. 'x³e°dxdy .3 OC. S x³e°dxdy O ...

A: NOTE: Refresh your page if you can't see any equations. . the limit of x is  the limit of y is 

Q: 2x – x3 da. = |- In(x – 1) + | Ftan-1(x)| + с Given: + J (x – 1)²(x² + 1)' 2(х-1) 2 2x – x3 determin...

A: Find your answer below