Consider the line L = {z = x + iy e C, y = 1} Let C = {w 1 -, z € L} with Convince yourself that C is a circle. Now C is centered at its radius being

Q: Calculate 8- Z dz, c z(4 – z) where C is the circle of radius 7, centre 0, negatively oriented.

A: Given that:∫C8-zz(4-z)dz, C is a circle of radius 7, centre 0, negtively oriented.

Q: 2. Assume the lines that appear to be tangent are tangent. Find ZW. Y 12 X 20 ZW =

A: Theorem  The tangent at any point of a circle is perpendicular to the radius through the point of…

Q: Let C be the positively oriented circle r? + y? =1. Use Green's Theorem to evaluate the line…

A: Just I have used the Green's theorem to change the line integral into double integral and then by…

Q: (b) Find a , b and c if the curvey = x + a x + b and y =c x + x have tangent lines paralle to each…

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Q: Let C be the positively oriented circle x? + y? = 1. Use Green's Theorem to evaluate the line…

A: Compare the integral ∫C19ydx+20xdy with ∫CMdx+Ndy to obtain M=19yN=20x Consider…

Q: Prove that the parabola y = x^2 at the points where the line has an angle of inclination "o" the…

A: Curvature of  a graph y= f(x)  k=d2ydx21+dydx232

Q: Evaluate | dz where c is the circle z| = 2. z (z+4)

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

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Q: Evaluate x ds, where C is a. the straight line segment x =t, y =. from (0,0) to (6,2) b. the…

A: We need to evaluate ∫Cx ds

Q: Evaluate the line integral . xy ds, where Cis the top half of the circlex +y = 16.

A: The given integral is ∫C xy2 ds, where C is the top half of the circle x2+y2=16. To find: the value…

Q: The curvature of any line with slope m in 2-space at any point on it is TTL

A:

Q: Evaluate ſſ, Vy² – x² dA where boundary of R is the parallelogram bounded by the four lines

A: In this question, we evaluate the double integral by using the change of variable. The region is…

Q: Let F(x, y) = x²e* i+ 60x²y² j, and let C1 denote the curve consisting of the line segment from…

A: Given:- F→(x, y)=x2exi→+60x2y2j→To calculate:- ∫C2F→.dr→where C2 is the line segment starting from…

Q: A solid is constructed between the graphs of y = f(x) and y = g(x) and the lines æ = a and æ = b so…

A: Given figure,

Q: Q2 Calculate 8- z dz, z(4-z)* where C is the circle of radius 7, centre 0, negatively oriented.

A:

Q: Let C be the positively oriented circle x2 + y² = 1. Use Green's Theorem to evaluate the line…

A: Given: C is a positively oriented circle x2+y2=1.  Objective of the question is to calculate…

Q: |Use Green's Theorem to evaluate | -x'ydx+xy°dy where C is the boundary of the C circle x + y =16…

A:

Q: for the reparametri zations alt)= (t, Cosht, o), tER. Find two Curve %3D

A: Given curve is αt=t,cosht,0 We have to find the reparameterization for the given curve.…

Q: If C is the line segment which begins at (-2, 1) and ends at (2, 4), evaluate the line integral: e+y…

A: Given, The line integral ∫Cex+yds Where C is line segment from the point -2,1 to the point 2,4 So,…

Q: The radius of curvature of the curve r = 4cos 20 at 0 = is %3D 4

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Q: Q2 Calculate 8-z dz, z(4-z) where C is the circle of radius 7, centre 0, negatively oriented.

A:

Q: What is the length of the latus rectum for the curve, (x + 3)2 + 4(y – 1)² = 4 а. 2 O b. 1 О с. 4 O…

A:

Q: =2) Calculate & ydx + xz² dy - zy³ dz, where c is the circle x² + y² = 4, Z=3 (conterclockwise)…

A: We will use stokes theorem to find integral

Q: If C is the line segment which begins at (-2, 1) and ends at (2, 4), evaluate the line integral: et…

A:

Q: Let C be the positively oriented circle x² + y² = 1. Use Green's Theorem to evaluate the line…

A: Greens theorem states that "for closed curve C enclosed a region R then the line integral along the…

Q: Consider the level surface 3x?y + 14z° = 3, the angle in degrees that the z-axis makes with the…

A: The given level surface: The angle in degrees that the z-axis makes with the tangent plane at point…

Q: Let C be the positively oriented circle x? + y? = 1. Use Green's Theorem to evaluate the line…

A: Given : C is a positively oriented circle x2+y2=1 We have to evaluate the line integral…

Q: Find the length of the curve. 2,3/2,0 st s9 x= 4t, y 3 61 242 2 3 O 2. seçenek 4. seçenek 122 61 3 3…

A: We can find the arc length as below

Q: Calculate Se(5x + 3y) i + (4x + 3y) j) · dĩ where C is the circular path with center (a, b) and…

A:

Q: 4. Evaluate the line integral / r y* ds where C is the right half of the circle r² + y² = 16.

A:

Q: Use Stoke 's Theorem to evaluate [ . dr, where v = y²i + xyj + xzk, and c is the bounding curve of…

A: We have to solve the given problem by using stokes theorem.

Q: Suppose a point X lies in the exterior of a disk, and suppose that two lines are drawn from X…

A:

Q: The curvature of y =x is

A: In this question we have to find the curvature of the given function which we can find out by using…

Q: 8. Let Ci denote the positively oriented boundary of the square whose sides lie along the lines x =…

A:

Q: Consider the level surface 2x2y + 9z = 3, the angle in degrees that the z-axis makes with the…

A: Given

Q: Evaluate the line integral | (x + 3y + 2)ds, where Cis the line segment joining the origin with the…

A: Solve integral.

Q: Find the curvature k of the circle C : (x – 2)² + (y+ 3)² 16 at the point (2, 1).

A: Use the formula of curvature to solve this problem.

Q: Find the length of the circle of radius r defined parametrically by x=rcost, y=rsint,0≤t≤2π.

A: Here I am attaching image so that you understand each and every step.

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

A:

Q: Let C consist of the part of the circle r +y = 4 from (2,0) to (0,2), Followed by the line segments…

A:

Q: 4. Let C be the positively oriented circle centered at the origin with radius r> 3. Without…

A: Given: Let C be a positive oriented circle centered at the origin with radius r>3. Without…

Q: Let C be the positively oriented circle x² + y² = 1. Use Green's Theorem to evaluate the line…

A: Greens theorem

Q: Find the curvature K of the circle C: (x - 2) + (y+3)² = 16 %3D at the point (2, 1).

A: Given: Equation of circle C: (x-2)2+(y+3)2=16 ⇒ (x-2)2+(y-(-3))2=42 We know that circle equation is…

Q: Let C be the positively oriented circle x² + y² = 1. Use Green's Theorem to evaluate the line…

A:

Q: Evaluate dV, where E lines between the spheres a+ y + z = 9 and E 2 + y2 + z? x2 + y? + z2 = 16 in…

A: The answer is in step 2

Q: the line integral SexY² ds where C is the of the Circle x² + y²=4 oriented clockwise Evaluate Cight…

A:

Q: Find the equation of the line tangent to the intersection of the surface z = arctan ry with the…

A: The tangent line to a plane curve at a particular position is the straight line that "just touches"…

Q: Let C be the curve connecting (0,0) to (9,3) to (-3,3) to (0,0) using straight lines. Evaluate (sec…

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Q: Evaluate the line integral: x dy – y da x² + y² where C is the circle x² + y? = a², a > 0, oriented…

A: