H-w lo Find the discontinnitypoint of &Cz): ニ 5(2+i) 2+ci-2)Z -2i fcz) = f cz) = Sin Z

Q: If (2) = u(x, y) + iv(x, y) is analytic in a domain D, then using first principles- that %3D dv du…

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Q: By how much will f(x, y, z) = e" cos yz change as the point P(r, y, z) moves from the origin a…

A: Given function is At origin,

Q: 1. In the following diagram, PA is tangent to 00 at A. If mBC = 50' , m/BEC=60', mBD=x and mAC = 2x+…

A: Since solve the first question for you. If youwant any specific question to be solved then please…

Q: Evaluate, using Cauchy's integral formula: sin tz? + cos Tz? () dz where C is the circle |z| = 3 (z–…

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Q: et zy = f sー n z = s %3D Ch) Find zqF zy White the sesubt on exact redangulet form,

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Q: w= Pcxiy,Z) = In (x+y+2) ,x= cost, and z = 4VE %3D 2X = y= Sint >use ch ain rule to Rind du in terms…

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Q: B. Evaluate sin z z²+j2z dz, C the boundary of the square with vertices ±1, tj clockwise.

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Q: Use Green's Theorem to evaluate (sin r + y) dr + (cos y +a?) dy, where C is the square con- sisting…

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Q: find the area of the surface S: x² + y² + 2² = 4 -A <tan -^ (*) FO 6 < COS Cos FJ VI (2) 4 DEX TI 3…

A: The given Surface is                    x2+y2+z2=4 ........1where π6≤tan-1yx≤π3 and π4≤cos-1z2≤3π4…

Q: evaluate by Sto ke's theorom Gcyzdx+ zx dy+ xydz),where Cis the Corve xày=1, z=y: [ Hint: §…

A: Solution:-

Q: Use Green's Theorem to evaluate (y? tan- a?) dx + (3.xy+ 4x – In(y² + 4)) dy, where C is the…

A: We need to evaluate integral.

Q: Evaluate the integral x² dx + y? dy where C consists of the arc of the circle x2 + y² = 4 from (2,0)…

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Q: Can you show the steps on how to do this integral?

A: Consider the provided question, (3) Evaluate the integral by using the greens theorem,

Q: The value of the line integral S(2xy dx + 2x?ydy + dz) C along a path joining the origin and the…

A: We have to find the value of given line integral.

Q: The common area between the cardioid r = 1+ cose and the circle r = 3cose is: Select one: (1+ cose)?…

A: For cardioid  θ=0,   r=1+1=2 θ=π2,    r=1+0=1

Q: O show mat me Nomal point @ X= a( Coro +o Smo) y= a(8in0-o Cor0) dy Sine %3D ep" of Normal S-ゴ」=…

A: the parametric function is x=a(cosθ+θsinθ) y=asinθ-θcosθ Differentiate each with respect to theta…

Q: 11. Evaluate 2 dA, where D is the shaded part inside the semicircle of radius 2 in Figure 26. 2…

A: To Find:  D is the shaded part inside the semicircle of radius 2 From the figure, the restrictions…

Q: Čopy of Given the following noninoar ordinary difforantial oquation, y+5y+2y2=f (1)· where f(t) = 3…

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Q: dz The value of the integral Jc 22+9 where c is the circle z - 3i| = 4 is %3D

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Q: Use Green's Theorem to evaluate the integral (3x² – y)dx + 3xdy where C is the circle a? + y? = 1…

A: As we know from the Green's theorem; ∫CMdx+Ndy=∫∫D∂N∂x-∂M∂ydA   Given; I=∫C3x2-ydx+3xdy So, M=3x2-y…

Q: 3 Use Green's theorem to evaluate [x³y dx - xy²dy, where C C is the unit circle x²+y=1 with…

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Q: Use Greens Theorem to evalua te the line integral Sr -93 dx +x*dy. where C is the positively onented…

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Q: Integrate counterclockwise around the circle |z – 6i| = 3. z(z – li)? - NOTE: Enter the exact…

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Q: 3. Find the circulation of F 2xi + 2zj +2yk around closed contour %3D

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Q: Transform the equation (ry? - z) dz + (z²y + y) dy = 0 into the form of separable dit %3D O ( + 1)…

A: Question is solved.

Q: dx Evaluate LJv by using Trapezoidal rule (up to three 1 + x? decimal places). [Ch-4(B), Expl-2]

A: We have to evaluate ∫01 dx1+x2 by using Trapezoidal rule.

Q: integrate ƒ(x, y, z) = sqrt(x2 + z2) over the circle r(t) = (a cos t)j + (a sin t)k, 0&lt;= t…

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Q: We have e+y dA = n(e-2) where B is the interior of t radius 2 and centered at the origin. Select…

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Q: 12. Use Greens Theorem to calculate P y'dx -a'dy C where C consists of the arcs y=x² and y =x1/2,…

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Q: 2 Use Green's Theorem to evaluate Jx*ydx-xy dy, where C is the circle 2+ y? – 2601 with…

A: Let be the vector field and C be the boundary of the region D. The Green's theorem states that .

Q: Evaluate the triple integral 2xe" sin z dV, where Q is the rectangle defined by Q = [(x, y, z)| 0…

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Q: Use Green's Theorem to evaluate the integral Sc(5 sin y – 3y, 2 + 5x cos y) · dĩ (6) where C is the…

A: (6) Use Green's Theorem to evaluate the integral ∫C5sin(y)-3y,2+5xcos(y)·dr→, where C is the line…

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: Find the unit fangent sector t for the currve : r=ti -2tj + 3t°k Y =a sin wt i +a Ceswt j %3D 2- r…

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Q: 15. Evaluate the contour integral e3z I (z+ 2)ªdz where C' is the circle |z| = . 9e6 2 O 27 9e-6 O…

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Q: 5. Evaluate (y +tan x)dx+(x -2ry+y)dy, where C is the circler +y' =4 and is oriented in a positive…

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Q: l, arctan( y/x) dA, where R = {(x, y) |1<x° + y° < 4, 0 < y< x} %3D

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Q: 2. Use Green's theorem to evaluate fe e-x³ dx + (5x + sin(y²)) dy, where C is the circle x² + y² = 4…

A: Please see the below picture for detailed solution.

Q: 10. (~Ch16 Review #17) Use Green's Theorem to evaluate | x?y dx – xy? dy where Cis ,2 the circle x2…

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Q: 8. PT is tangent to circle O at P If mNP = 90°, and mMXP : 186°, find %3D %3D X/ d. mZ4 e. mZ5 f.…

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Q: B. Evaluate sin z z²+j2z dz, C the boundary of the square with vertices +1, tj clockwise.

A: Evaluate the integral ∮Csin zz2+j 2z dz, where the path C represents the boundary of the square with…

Q: 1) (a) Evaluate |(2² – y°)dz +2rydy, along the circular C that is upper half-circle oriented…

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Q: H.w/ Findthe forthes tand closest paints.ah the sphere x+y+2'=36 from p(l2,2).

A: I used Lagrange Multiplier to solve this.

Q: UJ OUtall a COIIIIUCICE Imerval Ior po. Show that Oi – y) = , ới – y)? +E, Vi – ŷ;)² %3D |- %3D1…

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Q: 3.use Greens theorem s (1+x5 dx + 2xy dy ,where C is triangle With vertices (0,0),(1,0),(1,3)…

A: Apply greens theorem

Q: which of the sets is orthvoonal under the given inner product on C[0, T] ? = S fusgıx) dx I. {1,…

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Q: Find dyldy and xz4 Sint, y² Scost, OCtca24 For which vakes Of t is Hhe cure concave puars? anguer n…

A: x=4sint  , y=5cost

Q: Evaluate z dz, where the contour C goes from z = 0 to z = 1 to z = 1+i.

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Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.