Use Green's Theorem to evaluate the line integr y? dx + x • when C is the circle of radius 2 centered at the or

Q: Integrate counterclockwise dz, C the circle with z2 + 12z + 35 center –5 and radius 2. dz z2 + 12z +…

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Q: Use a projection to derive a formula for the distance from a point (x,y) to the line ax+by=c, where…

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Q: Describe the image of the line z = 1 + iy under the map flz) = sin z %3D

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Q: Verify greens theorem form 1 for F=x^3i+yj and c is the circle x^2+y^2=1, oriented anti clockwise

A: Find ∫CFdr, the line integral of F, where C is the circle x2+y2=1, oriented anti clock wise…

Q: Find the locus of the center of the circle touching the circle x\power{2} + y\power{2} − 4y - 2x = 4…

A: Let r and R be the radii of the required and the given circle,respectively.Let the center be…

Q: Parametrize the osculating circle to y = √x at x = 4.

A: Given that the osculating circle  y = x

Q: Consider the circle with the equation (x+2)^2+(y−1)^2=25 Its center is (           ,         )  and…

A: GIven equation:- x+22+y-12=25

Q: Where an Interior point Exists?

A: Interior point: Let S⊆ℝn.  A point a∈ℝn is said to be an Interior Point of S if there exists an…

Q: w=f(z)=z/(1-z) under transformation IzI=3 Find the image of the circle?

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Q: auchy - Goursát heorem to show that dz = 0 %3D 22 + 5z + 6 Cia tho girelo Lel hoth diroction

A: In this question, concept of Cauchy Goursat Theorem is applied. Cauchy Goursat Theorem If a function…

Q: Prove that the curve y: (-,-)→ R³ is regular with factor H and determine whether the image y (t) =…

A: If γ't not equal to 0 for all t∈-π2,π2then it is regular. If γ''t=kγ't for all t∈-π2,π2 then the…

Q: Evaluate |2*(x +7) – 2y ds C where C is the circle of radius 1 centered at (-3,0) and lying on the…

A: Since the integral ins on the plane x=-3 so the integral becomes:  ∫Cz3x+7-2yds=∫Cz3-3+7-2yds…

Q: Q3b): Compute zdz over several contours (i) The line from 1 to 1+ i. (ii) The circle of radius 1…

A: let fz=1z.  Since f(z) has an antiderivative in an open region D, then the line integral over given…

Q: Verify Stokes' theorem for the helicoid (1, 0) = First, compute the surface integral: = (VF)…

A: Given surface is helicoid whose vector parametric equation is \)" data-mce-style="cursor:…

Q: Prove that the locus of the point of intersection of two tangents to the parabola y? = 4ax, which…

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Q: find enclosed by following curves area Oくx(2て (a) 4= Cog x ;y=2- Cosx ; (b) y = X Sitx? Recall…

A: (a) y=cos(x), y=2-cos(x) Lets graph both equations using graphing calculator Area =∫abupper…

Q: Prove that the angle between the tangents from (a, ß) to the circle x² + y² = a² is 2tan ¹(a/√S),…

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Q: Evaluate  ∫C (3y + exsinx) dx + (8x - ln(y3+2)) dy, where C is the circle x2 + y2 = 9  with positive…

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Q: i y-jx x* + y* Q.5 (a) Compute |F.dr, where F and c is the circle x + y = 1 Use parametric equations…

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Q: Ex7 Circle (0, 1/2) Tangent to Circle (0, R) Show that AC=BC O A B

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Q: •Evaluate radius 2 25 where c' is a circle of 5²-1 centered at origin and directed cc W ds

A: We have to evaluate where is a circle of radius  centered at origin.

Q: Find the directional derivative of f(x,y,z)=xe +ye² at (0,0,0) in the direction of the vector…

A: As per our guidelines, I can answer only one question. To know rest please re upload particular…

Q: Prove that the equation of any tangent to the circle x\power{2}+y\power{2}-2x+4y-4=0 is of the from…

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Q: 3. Use Green's Theorem to show that to where C is the unit circle x² + y² = 1 in the…

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Q: Integrate counterclockwise dz, C' the circle with z² + 8z + 15 center -3 and radius 2. dz = La z2 +…

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Q: Find the equation of the tangent plane to the surface -2² at the point y = 2x2 – (0, –1,2)

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