Find the value of the derivative dy/dx at  t=2π/3 when an object moves according to the parametric equations:   x(t) = 2t+sin(2t) and y(t) = 3t−3cos(2t)   A) = 3+3√3 / 2-√3 B) = 2 - √3 C) = 3 - 3√3 D) = 1/4 (3 - √3)

Q: Find all harmonic conjugates of u(x, y) = x³ - 3xy² + 2y.

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Q: Find DF of fcxiy)=x²e° at the point (-2,0)-

A: Given function is fx,y=x2ey. We have to find the ∇f at the point -2,0. We know that ∇f=∂f∂xi+∂f∂yj…

Q: z 3e*3S,y 3z2 + sin(z)s G dx

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Q: The equation y =1-x² can be described parametricall by x = sin t, y = cos² t. %3D اختر احدى الدجابات…

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Q: Find the point D'4, symmetric of D4 with respect to the line F4B1. F4: (-2,1,3) D4: (1,2,3) B1:…

A: Here we will find poinr D'4 symmetric of D4

Q: How would this parametric function of x=2cost +cos2t; y=2sint-sin2t be solved

A: In order to solve a parametric equation, firstly differentiate x and y with respect to t and then…

Q: Provide a set of parametric equations for the function f(x) = x² sec² (2x + 1).

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Q: (77) (04-70° + 180² - 200+ 200+8) V = 0

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Q: 3. Find the derivatives: 3x3-4 a) f (x) = b) y = (x2 + 6x + 2) (+ Vx5 + 3) DO NOT SIMPLIFY 2x²+3 c)…

A: a) Use quotient rule of derivative and find the derivatives of above function.

Q: Function dy du dy du dx dx = (5x³ – 7x² + 2x – 3)*) _y = csc(x² – 3) y = 5x² – . y = V5x2 – 4 _y =…

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Q: Consi ider the ellipse 4x² + 2xy + 5y² The derivative = d on this curve is

A: Given: 4x2+2xy+5y2=149

Q: (D³ - 3D2 + 9D + 13)y = 0

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Q: (6) Find дл ду : ye+sin(2)=423 (8 points)

A: Explanation is given below:Explanation:

Q: d/dx (2x'y²+8x-2y+3)=? Select one: a. xºy2 b. 14x°y? O c. 14x®y²+8 С. d. 14x°y²+2y O e. 2x'y?+8x-2y

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Q: Find the direction field for the equation: y' = x + sin(y) + cos (x) at the point A = (0, pi3)

A: The direction field also known as slope field is used to graphically represent the solutions of…

Q: Suppose that I'm (f`∞x) = (x (24-1) and f(0) = 3-2i, f(1) = 6 -21, Find f(1+i)

A: Given that Imf'z=6x2y-1 To find: f(1+i).

Q: ex 3-4e2x 21) f dx

A: Given expression:  ∫ex3-4e2xdx

Q: 4) Find dy given: y (1-x)(1+ x )(1+ x³ )(1+x*) dx d'y given: y= (5x -3X7x+x) 5) Find dx

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Q: baseball is hit at 120 ft/sec from the ground at a 300 angle to the horizontal from a height of 3…

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Q: Find the solution. (D5 - 2D3 - 2D2- 3D - 2)y = 0. @ y = (c,+cx)e¯* + cze -2r + e*(c_,cosr + c zsinx)…

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Q: Graph the sinusoidal function using key points. 41) y = 1 + cos x 2- 1 -2n TC -1- -27 42) y = 4 sin…

A: Let's find.

Q: Calculate the imaginary part of  ∮C(Re(z)+3.78)(2z^2+ 5z+ 13 / z)dz  where C:|z|=1  Use FOUR…

A: We have to find the imaginary part of the integral ∮ fzdz, where fz=Rez+3.782z2+5z+13z over the…

Q: f(z) = 3z° cos(z) f'(z) =

A: To find f'(x)

Q: Prove that a parametric function given by I= 21 + 312 y = t² + 21 satisfies the equation dy + 2 dr…

A: see the details solution in below

Q: Subtract -2x'y? – 3x²y + 7 from 3x'y² – 4x°y – 3.

A: Subtract -2x5y2-3x3y+7 from 3x5y2-4x3y-3

Q: Consider the following equations: (a) y = 3x +7 (b) y + y = 0 (c) y/y= 232 (d) = 84x de (e) a2 + y?…

A: (a) and (e) are not differential equations.

Q: b) Find £{f(tu) e-3(t-u) cos 2u du}-

A: