Let B± = B¯(±1; 1 2 ), G = B(0; 3)−(B+∪B−). Let γ1, γ2, γ3 be curves whose traces are |z−1| = 1, |z+1| = 1, and |z| = 2, respectively. Give γ1, γ2, and γ3 orientations such that n(γ1;w)+n(γ2;w)+n(γ3;w) = 0 for all w in C − G.

Q: 1. Consider the family of curves 1 y = Vx +C Find its domain. Find the specific member of orthogonal…

A: first we will find the domain of the given function then we will find the differential equation…

Q: Let j=8 k=3 let A (0, 7-k), B(6, -k+5). Find all points P on the line y = 9-k such that AP I BP.

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Q: Write the coordinates of the vertices after a reflection across the line x = 2. F E D -10 10 10 D(3,…

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Q: Identify and sketch the graph of the following equations in R³ (a) x2 + 4y² + z² – 8x + 16y – 2z +…

A: we can add or subtract same amount from a equation to simplify equation. The logarithm function…

Q: 7. A curve in the zy-plane is described by the equation 2y(x − 1)² – xy² + 1 = 0. (a) Determine…

A: Given equation of curve: 2yx-132-xy2+1=0 Now, from the given points (1,0) , (2,0), (1,1) , (2,1) and…

Q: 2 1-Find the geometric location of the relation z – 3 -ži = v2. 3

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Q: Consider the curve defined by t and y = 2t² +6, for -2 ≤ t ≤ 3. Find an equation in x and y whose…

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Q: In the xy-plane, how many points on the curve y² + x² = 3 – xy have horizontal or vertical tangent…

A: The given curve is  y2+x2=3-xy

Q: 6a. Find . F dr, where F(x, y) = , and C consists of the circle x' + y = 4 from (2,0) to (v2, v2)…

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Q: 4. Find all integer-valued points on the curve C given by the equation x² - 2x + y² - 4y = 620.

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Q: use the given graphs of x = ƒ(t) and y = g(t) to sketch the corresponding parametric curve in the…

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Q: Find F-dX where C is the curve X(r) = r°I+( 2r+ 1J, 0<I55, and Fxy) = rI+yJ.

A: 9

Q: Sketch a contour map and graph of . a. g(x, y) = 9x² + 4y² b. z = y/x

A: The given function is: g(x, y) = 9x2 + 4y2 The contour map of the above function is:

Q: (3,-4,-2) Show that 323 f dx + gdy + hdz = f(-3) 12x²y^z²dx + 16y³x³z²dy + 8zy r³dz is independent…

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Q: .Sketch the level curves z=k for the indicated values of k = = =— (x² + y²), k =0,2,4,6,8

A: The equation x2+y2=a2 reperesnts a circle of radius a with center at (0,0) .

Q: Let d1 and d2 be the distances from the point (x, y) to the points (−1, 0) and (1, 0), respectively,…

A: The distance between two points x1,y1 and x2,y2 is defined by the formula d=x2-x12+y2-y12. Given…

Q: Let 13 20 x 20+ y = 2 be the equation of a curve in the xy-plane. Find the equation y = T(x) of the…

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Q: -2 B-BL and u= 6 -1 Compute the distance d from y to the line through u and the origin. Let y d= = =…

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Q: 1. Sketch the graph of the domain of the function f (x, y)= sq x / x−y​ 2. Compute the equation of…

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Q: Let C be the curve.

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Q: Find an expression for dy in terms dz x² + y? + 8x 14y = 33 Using the dy found above find tho

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Q: 4. Locate the fixed point of x = xy y = x + y and compute the index about the fixed point.

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Q: Consider the curve defined by x = t - 4 and y = t² + 3, for -3 ≤ t ≤ 4. Find an equation in x and y…

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Q: E.g. Let f(x, y) = x² - 2xy + y². The graph and contour diagram of f is given below right. Compute…

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Q: 34. A half-turn about (3, 2) maps P to P'. Where does this y half-turn map the following points? (3,…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Evaluate √ zdz xdx + xydy + (x+z)dz where C is the line segment from (3, 1, 3) to (4, 2, 2).

A: First we calculate the line segment between two point and convert x,y,z variable to one variable t.…

Q: For what values of k does the family of curves =² + (y – c)² = kc² have an envelope?

A: Eliminate C from f and f'c

Q: he curve y = X fc (vî (yi

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