QUestion: what do you notice? ® SS Uxy2 dA , R= [2,4] x C1,2]

Q: Find the area inside the circle r = 6cosθ and outside the cardioid r = 2(1 + cosθ).

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Q: dz at the point (3,2, 1), where z is defined implicitly by the equation z +z²x² – y = 8 Calculate dx…

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Q: $(r, 0) = (r cos(0), r sin(Ø), 0), 0 <r< 1, 0<0< 2a S(x, y, z) = Vx? +j + y? ymbolic notation and…

A: Introduction: The surface integral is used in mathematics to add a collection of values associated…

Q: F(x, y) = (y cos(x) – xy sin(x), xy + x cos(x), Cis the triangle from (0, 0) to (0, 6) to (2, 0) to…

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Q: X=r sinø cose y=r sinø sine z=r cosø p² = x² + y² + z² Determine a, y ,əz , ə, ,dg,dg

A: Given that: x=rsinϕcosθy=rsinϕsinθz=rcosϕr2=x2+y2+z2 In partial derivatives, except for the variable…

Q: a) Find the area of the reason that lies inside the circle r = 3a cos 0 and outside the cardioid r=…

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Q: 2. y=2/x, y=8x, y=(1/8)x, x>0. FIND IT'S AREA

A: Given y=2x, y=8x, y=18x, x&gt;0

Q: X-y verity that %3D di Y=Ce* IS a solurion

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Q: 16. / cot(z) dr 17. cot (x) dr 18. csc(r) dr

A: (16) ∫cot(x)dx ∫cot(x)dx=∫cosxsinxdxPut t=sinx      dt=cosxdx we get-∫cot(x)dx=∫1tdt…

Q: Deseribe the transformations applied to y = sin x to obtain y = 2 sin(3x +5) + 1. %3D %3D

A: Solution

Q: Using De Moivre's theorem determine z= 3+6i^4

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Q: 2 point Find the integral: / = I. (cosax cosnx ) dx a sinan cosn a². 2a sinan cosn (A) I = (B) /…

A: Given that  The integral  To determine the integral

Q: ied region. on r = 4 + 2 sin e B) 367 - 16 4) C) 187 D) 367

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Q: Ise the areas shown in the figure below to find the following. y = f(x) Area =0.6 Area =1.1 a /c d…

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Q: (positive) angle of 45° with the positive x-axis. (f(x, y) = In(4x2 + 10y2) fonksiyonunun (v2, v2)…

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Q: sin?(Væ) + cos (V)) dA, where R= [0, 2] × [0, 2]. R

A: The given integral is: I=∫∫R sin2x+cos2y dA,       where R=0, 2×0, 2

Q: 5 Find the area of the surface Surfe the r hemisphere The part of t that lies between the circular…

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Q: 1 (z + 1)(z – 1)²(z – 3)? - 3 p(x) = %3D - a) Degree: b) Right hand end behavior: As a ? v c) Left…

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Q: DW Test:   Given DW=0.54, what is rho (hat)?

A: Given data DW = 0.54

Q: e integral be 'solvable' using trigonometric substitution. What is the correct choice of u given J…

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Q: Using trapezoidal, and 3/8 simpson's rule ⌠13 (1.2x3 + 0.3x2 - 2)dx

A: Given that, ∫131.2 x30.3 x2-2 dx is the function we have to solve it by using the trapezoidal and…

Q: 2. Evaluateſff, y dV, where: E = {(x, y, z) | 0 <x< 1,0 < ys4x, y szsx? + y} %3D

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Q: Selue ( frendz, whee frz)= 2z z,c the unit az"-Z, C %3D Cindo Countacdocture)

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Q: 7/2 0² sin 20 d0

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Q: 2) reflection across the y-axis y

A: Reflection across y-axis Rule: (x,y)→(-x,y)

Q: bordinates where R: 0 < aw the solid R. th 2 2

A: We will use relation between Cartesian and cylindrical co ordinate system to get integral  x= r cosθ…

Q: cot z• 2z dz In sen z' + c 33. cot x' dz %3D 1/2

A: see below the answer

Q: se Green's Theorem to evaluate Je(*+y* ) dx +(x-y')dy Cis the triangle with vertices (0, 0), (2, 1),…

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Q: e center of part B measured from x-axis is (mm) - 400 mm- 50 mm 200 mm 50 mm 50 mm elect one: O 25 O…

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Q: S(csc z cot z + 7x®)dr = - csc z+z + e O - csc z - +c O cot z+z7 +c O csc z +x7 +c CSC z - z +c

A: We will use integration to solve the given problem .Hence, first option is correct.

Q: of the F (x,y)=5 y

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Q: (a) Write down a formula for the volume V of the solid obtained by revolving the region R about…

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Q: I? How is charge difference related to current Select the correct response: I = RLQ 1 Q o I = DQ o I…

A: (4) We know, I = dQdt Hence,I = DQ,   where D = ddt (Third option is correct.)

Q: Area inside the circle r = 2sin θ but outside the cardioid r = 1 + sin θ.

A: Given: Give equation of the circle r=2sinθ and the cardioid r=1+sinθ We want to calculate Area…

Q: sin' Acos e de. (b) cosA de. Aus. (a) 37/256. (b) 5T/8 Evaluate (a)

A: (a). We use Gamma function to evaluate the given integral. (b). We reduction formula of cos(x), to…

Q: iv.y %3D cot1 (x), у € [0, п] v.y = sec-1 (x), y e |-1, – u|0, vi. y = csc=1 (x) , y € [-T, – U [0.…

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Q: 6. y = sin x, y = x, x = TT/2, X = TT

A: Consider the curves

Q: cosh(z) Evaluate 6- dz, where C:|z– 2i|=1, counterclockwise. - 4

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Q: tan 0-2cos 0 tan Ocos 0-2cos 0 A) 0, x) В) 0, л, 3 5л 7л C) 6 6 D) n B O A O D

A: I am going to solve the problem by using some simple trigonometry to get the required result of the…

Q: parar rameter value ənre SA(z) = A sin z, = 1 %3D ·Es(2) = de*, 1 = 1/e Ex(2) = de, d = -e . Qe(x) =…

A: (d). Given, Qcx=x2+c;  c=-34 First of all let us find the fixed points. Qcx=xx2+c=xx2-x+c=0

Q: A LMNIS the result of a reflection of A XYZ y across the y-axis. 6. Which angle in the image…

A: Since the given triangles are the mirror images of each other. Hence the angle which looks the same…

Q: r= a(1 – cos 0) is called a The cardioid has equation (x² +y² + ax)* = a°(x? + y*) %3D

A: This is a problem of curve tracing in polar form.

Q: The area of the region that lies inside the cardioid curve r = cose + 1 and [(cose + 1)² = cos²0]de…

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Q: %3D %3D 2 value of y' by usiny Cs amer's Rele?

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Q: particular solletion e 18e se +tuish =ht, h-

A: We will find out the required solution.

Q: Find p, q if f," f(x) dx + Si2" f(x) dx = [,' f(x) dx. %3D (Give your answers as whole or exact…

A: Given,

Q: g(z) : nction defined on R by %3D 1+.Write ar ermine its domain. Explain your reasoning.

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Q: TOÀN THỊNH PHÁT 2 Calcule the surface area of the core 2 = 3√x ² ty ² lies between the two 2 planes.…

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