1) Evaluate F dr where F(r,y) = ri and C is the half of the circle %3D ²+y 3 16 lying below the r-axis, oriented counter-clockwise.

Q: Identify the following surfaces and sketch. a. x² + 4y² – 4z² – 6x – 16y – 16z + 5 = 0 b. 5y = -z2 +…

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Q: B- Find all local extreme values of the following surface. f(x, y) = 2xy – x² – 2y? + 3x + 4.

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Q: In what plane does the curve r(t) = t i + t2 k lie?

A: r(t) = t i + t2 k We need to find the plane of the curve located in?

Q: Let C C R? be the path from (3, –2) to (3, 2) along the graph of the curve x – 5x?y? – 7x2 = 0.…

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Q: 5. Let C be the circle x +y} =4_which is positively oriented. Let C, be the upper half-circle C1 =…

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Q: The tangent line to the graph of y = In(2x) is perpendicular to z + 4y = 1 at the point where Select…

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: Identify and sketch the graph of the following SURFACES. x² + y² = sin² z, Z = [0, π]

A: Given.   x^2+y^2=sin^2z

Q: 4. Consider the curve in the plane defined by r3+y3 = 6xy. %3D (a) Find for any point (r, y) on the…

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Q: Verify Green's theorem for F =, where C is the part of the parabola y = x², and the line y = 4 for…

A: If be a positively oriented,  closed curve  enclosing the region D Then for a vector field F→=P,Q…

Q: F· dr, where F(x,y) = –lj, and C is the part of the graph of y = - x from (2,2) to (–2, C

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Q: Find the linear approximation at x = 0 to Write %3D 2- your answer in the form y = Ax + B. %3D

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Q: draw and identify the graph of the following surfaces a. x² + y² = sin²z, z = [0, π]

A: Any surface in the 3D plane can be represented in the form of f(x,y,z)=0. A graphing utility can be…

Q: - Graph the surface 1 = y² + z² — by first sketching at least three cross sections in each of the xy…

A: To Plot: Graph The Surface 1=y2+z2-x24 by plotting at least three cross section in xy and yz plane

Q: Use cos(t) and sin(t), with positive coefficients, to parametrize the intersection of the surfaces…

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Q: D A Find thepolar eavation for the cartesian curve (x²ty) - A)r-4 cos o =4x. Br°=4 cos e c)r?=4cos o…

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Q: 4. Let C be the unit circle in the xy-plane, and S be the boundary of the square with side 1,…

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Q: A surface in R³ is defined by the equation 4z = x² + 4y“.

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Q: Use cos(t) and sin(t), with positive coefficients, to parametrize the intersection of the surfaces…

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Q: 2) Consider the oriented curve C given by C = C1uC2, where C2 is obtained by intersecting the…

A: We will first parametrize the curves C1 & C2 then substitute the x,y,z values into the line…

Q: 6. Let C C R? be the positively-oriented boundary of the graph of the circle x2 + y? = 1. Using…

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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: 7. Given that the line y = r -b is an asymptote to the ar curve y a,b €R,rz 1, then b = A -1-a 1-a C…

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Q: Find the points on the surface z2 = xy + 4 closest to the origin.

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Q: C is the intersection curve between the paraboloid z=x²+y² and

A: Given that C is the intersection curve between the paraboloid z=x2+y2 and the cylinder x2+y2=1.

Q: A surface in R³ is defined by the equation 4z = x² + 4y².

A: Given:-                 The surface in  is given by  . Sketch the intersections (traces) of this…

Q: Given F(x, y) = [arcot(/K)-(secx)* - 2y]i+ 3x-es 2021 evy and the curve C=C,UC,UC, as shown in the…

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Q: Let F = (tan(3x) - y)i + (2x – sec-1y)j and C be the boundaries of the circle x2 + (y-4)2 = 9 in the…

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

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Q: 4. Evaluate y ds where C is the upper half of circle x² + y² = 9, traversed in the counterclockwise…

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Q: Find . F.dr when F(x,y) = (2x,3y²) and C is only the first quadrant part of a circle of radius 3…

A: Let C be a smooth curve and r→t=xti^+ytj^+ztk^ be the position vector of any point x,y,z on C.…

Q: Let F = (tan-(3x) – y)ỉ + (-2x + sec¬1y)j and C be the boundaries of the circle x? + (y – 4)² = 9 in…

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Q: 3. a) Compute: f (Rez-32) dz where I is a directed line segment from z=0 to z=i. b) Let C be the…

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Q: Evaluate f 3z2dz over C, where C is the upper half circle |z – connects points O and 1+i. -글히 %3D플…

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Q: Find the extreme values of the function ƒ(x, y, z) = xy + z2 on the circle in which the plane y - x…

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Q: /| 9(x + y) dA where R is the region that lies to the left of the y-axis between the circles x2 + y?…

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Q: 3. Evaluate ff, (x² + y²)³/²dA, where D is the region in the first quadrant bounded by the x-axis,…

A: Given problem:- Evaluate ∫∫D (x² + y²)3/2 dA, where D is the region in the first quadrant bounded by…

Q: i) Use the residue theorem to evaluate 2z+6 dz, where c is the circle |z – i| = 2. z²+4

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Q: Let F (tan-(3x) + y)i + (2x + sec-ly)j and C be the boundaries of the %3D circle x? + (y- 4)2 = 9 in…

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Q: Verify Green's Theorem in the plane for F = -3y³i+ (3x3 + cos y)j where C is the circle x2 + y? =…

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Q: EVALUATE § 7. d² USING STOKE'S THEOREM 3xz^ + ex² ₁ + 2xy^ с F(x, y, z) = 3XZ1 te C IS THE CIRCLE…

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Q: in R°sketch the graph of the cylinder x = (y – 2)?

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Q: 3. Show that every sphere through the circle x2 +y-2ax+r²=0, z=0 cuts orthogonally every sphere…

A: This is a co-ordinate geometry problem

Q: Let F = -2yi + 2xj. Use the flux form of Green's Theorem to compute F·n ds where C is the positively…

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Q: Consider the intersection curve C in the first octant, between the surfaces s1: 2 = 1- r? S2 : 2 +…

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Q: Let Q = 4x2 + 6xy+ 4y? . The points on the curve Q = 7 which are closest to the origin are: %3D %3D…

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Q: Verify Green's theorem for F =, where C is the part of the parabola y = x², and the line y = 4 for…

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Q: Evaluate |(y zi+y°i+xzk)•d$ where S is the boundary of a cuboid defined by S -15x<1, -1<ys1 and…

A: The given integral: S=∬s(y2zi→+y3j→+xzk→) dS Where S is the boundary of cuboid defined by -1≤x≤1,…

Q: T 1) Reflect quadrilateral ABCD across the y-ar reflection on the coordinate plane to the right. new…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: On the surface z =, in what direction is z increasing most rapidly when x =1 and y = 2.

A: A function z=f(x,y) increases most rapidly, at a point (a,b) , in the direction of the gradient…

Q: At which points does the curve r(t)=ti+(2t -t² )k intersect the paraboloid z = x² +y? ?

A: Given: r→t=ti^+2t-t2k^ and z=x2+y2