Use trigonometric form to find z1z2. and z1/z2, given that z1 = -2 + 2¡V3 and Z2 = V3 + i. %3D

Q: Find ди ds if w = sin(xyz), x = 1 - 3t, y=e¹-t, and z = 4t, find o

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Q: V2 2. 2.

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Q: Evaluate dx 1²√√²-49) SV x>7, using a trigonometric substitution.

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Q: The appropriate trigonometric substitution for dx is 3r-r2

A: To find:∫13x-x2dx

Q: Find the quotient of z1 & z2, leave answer in trigonometric form: z1 = 2 – 3i & z2 = 1 – V3i

A: Introduction: Division is also performed between two complex numbers. But in order to convert the…

Q: 4r2-8)3/2 dz

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Q: use the disTance Formula to Find the distonce between (e)and(3,2)

A: We use the distance formula to answer the given question.

Q: Find the area inside one petal of the four-leaved rose r = sin 2x

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Q: Find the length of the cardioid r = 1 - cos θ.

A: Arc length in polar coordinate is given by:

Q: Find the angle (in radian) between the planes 2x + Z = 3 and x + 2y + Z = 2y z = 2.

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Q: Find Duf at P. f (x, y) = sin(4x - 4y); P(4, 4); u = j %3D NOTE: Enter the exact answer. Duf = %3D

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Q: : Find the length of the cardioid r = 1 + cos 0 0 < 0 <T

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Q: Write the DE, e" y' + e2y= sin a in the general form.

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Q: Evaluate using the substitution u = 1 − x2 or trigonometric substitution.

A: Given: ∫x1-x2dx  ……1

Q: Given that z = 4 ( cos· 4 +i sin) and w = 1 – iv3. Find 4. %3D a) 2 w b) E c) arg (-), in radians as…

A: Since you have asked a question with multiple parts in a single request, we would be answering only…

Q: Evaluate the integral (Trigonometric Substitution) 1 (b²y6 – y³)źdy

A: SOLUTION-

Q: Solve the following trigonometric equation for 0sxs27. Show your work. 2sin x+5sin xr -3 =0

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Q: Find the tangent of ZD. 3/3 2V10 E Write your answer in simplified, rationalized form. Do not round.…

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Q: dx If x2 - 2x – 4 is solved by trigonometric substitution, which of the following substitutions is…

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Q: find an appropriate trigonometric substitution of the form x=f(t)x=f(t) to simplify the integral…

A: Here, we use the substitution x=(sect)^2, as we know sec^2t=1+tan^2t, so x^2-1=tan^2t

Q: Find the solution(s) for theta. V2 cos O (30, 225, 330} O (135, 225} O (30, 135, 330} 0 (30, 225}

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Q: If v = 3i - 7j and w = -i + 4j, find the magintude of w - v. Round to one decimal place.

A: Given query is to find the magnitude of the following vector.

Q: 2. Vy+1-2 dy

A: ∫vn dv = vn+1n+1+C

Q: Using the substitution z = tan 0, evaluate dz, V81 + 4z²

A: The given integration is: ∫181+4x2dx  To evaluate the given integration.

Q: c) If f(x, y)= e" cos 2x, then show that = 0.

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Q: Q5) chang e the Po lar 2r=2+cos o.(2r-1) to Cartesian

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Q: U is y= cosx. A

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Q: Use this reduction formula and your answer in part a) to find ſ cosª xdx and ſ cos® xdx.

A: To find ∫ cos4 x dx and ∫ cos6 xdx First we find ∫ cos4 x dx Apply integration reduction…

Q: u(x,у)- (sin x)(e' — е").

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Q: Show that r = cos20 is symmetric about the y-axis.

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: (b) Find the entire length of the cardioid r = a(1+cos0).

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Q: a) Find dz, if z = e' sin e %3D b) Verify uxy = uyx , if u = In /x² + y² . %3D

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

Q: The þaramehc equalion of the unde x+ =9 is ☺ x = 9 cost, y=9 sint X = 3 cost, y= 3sint X = 3 cost,…

A: A circle is a two dimensional  shape an it is  a closed curve . A set of all the point are at the…

Q: For the integrand Va2 + 6462, b>0, which trigonometric substitution will be used? x =| %3D

A: →If we have any expression of the form x2 + a2 , then                             Use x = tanθ as a…

Q: Find Duf at P. f(x, y) = sin(6x – 4y); P(4, 6); 4 3 i u = j JOTE: Enter the exact answer. Duf =

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Q: Use Green's theorem to evaluate $y – sinx)dx + cosx dy Where c the triangle of the adjoining figure…

A: Green`s Theorem:-  Green`s Theorem states that the line integral is equal to the double integral of…

Q: Evaluate the following using the TRIGONOMETRIC SUBSTITUTION METHOD: 1.5 dx

A: Given: I=∫dxx2x2+4 For evaluating given integral, we substitute x=2tanθ…

Q: Find the left most point on the upper half of the cardioid r=1+cos(theta)

A: we need to find leftmost point on the upper half of the cardioid r = 1 + cos(theta) by plotting in…

Q: sketch r= la 2 Sin'co+)

A: r=1-2sin2(θ+π3)

Q: Using a trigonometric substitution, the integralC V 16 da becomes: Select one: tan20 O a. - Ja/4…

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Q: • Graph the cardioid r a(1+ cose), a < 0? %3D

A: the graph of given  cardioid

Q: • Find a harmonic conjugate of u(r, y) = x² – 2x – y². Show that u(r, y) = e" cos y is harmonic.

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Q: Determine c1 and c2 so that y(x) = c1 sin 2x + c2 cos 2x + 1 will satisfy the conditions y(pi/8) = 0…

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Q: Given, a(x,y,2) = 23x3 tan (y) + x*29 %3D Find the expression for Izyz and Caleulate it at the point…

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Q: Find the length of the cardioid r = 1 – cos 0.

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Q: Find a trig substitution r = f(@) that makes 1 dr = cos 0 de. (V4+)3

A: Here we have to substitute x =f(θ)

Q: Find the angle (in radian) between the planes 2x + 2y Z = 3 and x + 2y + Z = z = 2.

A: Consider the two planes: 2x + 2y - z =3  and  x + 2y + z =2. We have to find the angle between the…