Q1/Prove that the polar expression for the function y = Vx2 - (x2 +y2)3/2 is r = cos20

Q: 2. Compute dy dx (x² + y²)' by first changing it to polar coordinates.

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Q: 4–x2 Sở SY dy dx using polar Evaluate 2x-x2 Coordinates.

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Q: Find z in 2= Sinh (4-j5). cos (4-5) express in polar porm

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Q: 2- find if z = x + 2メッ ze %3D U COSU = u sinv

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Q: Qss- Prove that fcz) = cx=y') + ( are harmonic function of C, y) ,but are not . hormonic conjugates.

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Q: Compute the derivative dydx of the polar curve r=sin2θ at θ=π3.

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Q: find the volume of the solid

A: Find volume of solid.Sketch the given function.

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

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Q: x³y"+xy'+4y = cos (2 In x)

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Q: Find the general solution of y'=cos²xcosy

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Q: Q2 : Express the function r2 +r(sin0 + cos 0) = r² sin² 0 by %3D cartesian form

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Q: Each of the two functions v and u with the variables x and y satisfy he Cauchy - Riemann equations,…

A: Let,  u=x2-y2, v=2xy

Q: 41-44 Use Theorem 13.5.3 to find dy/dx and check your result using implicit differentiation. 42 x3 –…

A: Implicit differentiation

Q: Suppose that 2x² - y² = t² and x = t cos 0. Find (a). ¹(2), X and 0

A: answer is in next step

Q: Eliminate the parameter to find the cartesian equation of the curve: x = 2 sin 0, y = cos² 0, sos…

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Q: Find the 1st  and 2nd Derivate of y with respect to x from parametric equations. Complete solution…

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Q: 1. x (0) = 0 + cos 0 y (0) = 1+ sin 0 given that

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Q: Evaluate fs xyz dS where S is the triangle with vertices (1,0,0), (0, 2, 0), (0, 1, 1).

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Q: Graph the curve r2 = 4 cos θ in the Cartesian xy-plane

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Q: 5(a) Find the slope of the tangent line to the polar curve r = 2sin0 -3cos0+1 at 0= 1/4

A: Using slope formula we have

Q: find the decomposition of a(t) into tangential and normal components at the point indicated r(0) =…

A: v⇀(θ)=r'⇀θ=-sinθ,cosθ,1a⇀(θ)=v'⇀θ=-cosθ,-sinθ,0…

Q: Find the slope of the tangent line to the polar curve r = 2 – sin(8) at the point specified by 0 =…

A: Note: As per our guidelines issued by bartleby we should solve only one question each time, so…

Q: Eliminate the parameter t from the parametric equationsx =3 +sin t and y = cos t - 2.

A: Given: x=3+sint and y=cost-2 We have to eliminate the parameter t from the parametric equations.…

Q: 4. Find the parametric equation of the tangent line to r(t) = 4costi – 3tj %3D at Po(2, –n)

A: Given: To find the parametric equation of the given tangent line as follows, r(t) = 4 costi- 3tj…

Q: Q2 Q2/If y = (x³ + 5x² + 1)3 + Jsin+/cos³Vtan3x2 find y'

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Q: Show that the Euler-Cauchy Equation ry" + ary + by = 0, r+0 can be transformed into the constant…

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Q: 1.5 3-X Evaluate the integral *dy dx using polar coordinate

A: Follow the procedure given below.

Q: Compute e4 cos (r – 3) dr with two decimal places. Number

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Q: i. Jsin xcos 2x - sin 2x cos xdx

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Q: 1z2 in polar form. z1 = 5(cos(170)+i sin(170)) : z2 = (1/2) (cos(10)+i sin(10)

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Q: The derivative Z of the parametric equations z= 7 sin 3t and y= cos 3t is.

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Q: 3Tt of cSC X du If u = f(x), then dx cos X . Compute %3D 2 sin x и -

A: Given ,  u = f(x)

Q: Find an equation y = f(x) for the parametric curve c(0) = (cos(0), 3 cos(0) + 8 sin²(0)) and compute…

A: The objective is to find y(x) and it's it's derivative .

Q: Q1/Prove that the polar expression for the function y = Vx2 - (x2 + y²)3/2 is r = cos20 Q2/Find the…

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Q: Determine an equation for the sinusoidal function shown. 2. 12 21 Oy = 0.5 cos[0.5(x+ x)] + 1.5 Oy,…

A: The general equation of a sin function is given by; y=A cos(Bx+C)+D Where; A→Amplitude of the…

Q: The x- intercept of the tangent line to the polar curve r=3(1+sin 0) at 0=" 프 is

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Q: Verify that y = 7 sin 2x + 9 cos 2x is a solution of y" + 4y = 0 %3D

A: Given, y = 7sin2x +9cos2x  We have to verify y = 7sin2x +9cos2x is a solution of y"+4y = 0

Q: 4) z = (4 + j3)sinh(3+j)+cos(3-j2)

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Q: determine the slope of the tangent line to the polar curve r = 3 + 8 sin 0 at 0 =

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Q: 3. Which of the following is the equation of the tangent () line to the polar curver = sec at the…

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Q: ) Compute f-(, ") and fy(§, T) of f(r, y) = e9 cos(ry)

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Use Cramer's rule to solve for x' and y' in terms of x and y. x = x' cos 0 – y' sin 0 y = x' sin 0 +…

A: Solution is given as below:

Q: Cos 4x b. .J dx,u=1+2 sin4x (1+2 sin 4 x )*

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Q: If A =x 2sinyi+z?cosyj -xy2k then -=x?cosyi - z?cosyj-2xyk 1O ду =x?cosyi-z2sinyj-y?k ду .II O…

A: We use partial derivatives to answer the given question.

Q: Find the second derivative of y with respect to x from the parametric equations given. x = 3 + 4…

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Q: The velocity of a particle moving in the xy plane is given by the parametric equations dx/dt=…

A: The given parametric equations of the particle is dxdt=-2t sin2t and dydt=2t cos2t. Evaluate the…

Q: The integral (cos(3x)) sin(3x)dx under the change of variable u = cos3xbecomes v uz du. -9/29 Select…

A: Given,