*6. Let f: R' →R be given by =+4x'z-6xyz+4y-3x'y. Is M=f-((0}) a smooth surface (2-dimensional manifold)? If not, at what points does it fail to be so?

Q: 13. Find the area of the surface generated when the curve y = -, on [2,4] is rotated about the…

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A: we need to find gradient of given surface to know about direction of normal vector to tangent plane

Q: Find the equation for the tangent plane to the surface z=ln(4x2 +3y2 +1) at the point (0,0,0)

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Q: Find the tangent to y = cotx at x = - T O A. y = - 2x + 2 π +1 +1 OB. y=2x-- OC. y=2x+1 OD. y=-2x +…

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Q: 2) Evaluate the vategral if cis any Seetion al Smooth Curve from 10,0,0) to (lilil). .(-3p²+2y-Z) da…

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Q: Find the uolume of the soild olbtained by the grophs bounded by potaling the begion Y = x² +1 and Y…

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Q: 4. Find the equation of the tangent plane to the surface Z = = 5tan(x) – sin(3y) at the point (xoyo)…

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Q: 7. Find the area of the surfaces generated by revolving the curve r = 2e®² for 0<0s- about x- axis.

A: The solution are next step..

Q: 6) What is the tangent plane of f (x, y) = 5x² – 2xy? + 3xy + 4x at point (xo, Yo) = (1, –2) ?

A: The question is solved in step. 2

Q: 2. Find the slope of the tangent in the positive x-direction and y-direction to the surface z = 2xy…

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Q: 2. Use Green's theorem in order to compute the line integral P (x – 4)³ dy – y³ dx where is the…

A: We need to compute the given integral using Green's theorem . ∮C(x-4)3dy-y3dx Where is the circle of…

Q: find the to the the tang horizontal. X-volves at which the _9x+2 Y = ex curve ent

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Q: 4. Evaluate the line integral 6. x²y dx – xy² dy where C consists of the arc of the circle 16 = x² +…

A: Given equation of circle is  x2+y2=16x2+y2=42 radius is 4 We have to calculate line integral ∮ cx2y…

Q: If f=2yzj -zj+xk,evaluate line integral Fxdr along the curve x=cost,y=sint,z=2cost from t=0 to…

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Q: Find the points on the surface ry + yz + zx – x - 22 = 0 where the tangent plane is parallel to…

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Q: Evaluate the line integral (direct method) | (3x– y) dx – x dy , where C consist of the parabola…

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Q: Evaluate the line integral Fdr where F = 4.xyi – 8yj+ 3k and C is a curve given by y = 2x, z = 3…

A: Answer

Q: #3) Find equations of the tangent plane to the given Surface at the specified Põint. X + y +Z=42VZ…

A: Find the equation of the tangent plane.

Q: 2. Set up the formulation to find the surface generated when the curve y=x is revolved about the…

A: Let f(x) be a nonnegative smooth function over the integral [a,b]. Then the surface area of the…

Q: If F(x, y) = (6xy - 1,3x2 + 2y) and C is the circular arc along x² + y? = 2 from (1, 1) to (-1, 1),…

A: Given vector field is  F(x,y)=6xy-1,3x2+2yF(x,y)=(6xy-1)i+(3x2+2y)j c is the circular arc along…

Q: Evaluate the line integral F. dr, vhere F(z, y) = -yi-rj and C is the curve y = v4-a from (2,0) to…

A: We have to find the line integral

Q: Find an equation of the tangent plane to the surface x² + 2y² + z² = 175 at the point (5, -5, 10). O…

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Q: Show Z=arctan(y/x) satisfies Zxx+Zyy=0.

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Q: The tangent plane to the graph of the function f(x,y)=x+xy+y2, which is parallel to the z=1+2x+3y…

A: Here given surface is fx,y=x+xy+y2 or x+xy+y2-z=0......1 Then, consider Fx,y,z=x+xy+y2-z

Q: 1_2 Can you please help me with this example in a step by step guide. Thank you very much!!

A: To calculate the coordinates (x,y,z) and also define the absolute extremum for the provided surface…

Q: Evaluate the line integral Jo 9x²yzds with respect to s along the с 2 curve C: x=t, y = t², z = /t³…

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Q: 4. Find the equation of the tangent plane to the surface ew + In(xz) - evz = 0 at the point (1,0,…

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Q: 5, find dt when r = 3. dt Let A be the area of a circle with radius r. If %3D %3D

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Q: Find equations of the normal plane and tangent line to the curve of intersection of the surfaces…

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Q: Find the area of the Surface generated by revolving the given curve about the - axis while x is over…

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Q: 3. Find the exact area of the surface resulting from rotating y = v1 + e* from x = 0 to x = 1 about…

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Q: 4. Find the equation of the tangent plane to the surface ey + In(xz) – evz = 0 at the point (1,0,…

A: Given:

Q: 9) Find a point on the surface z = 8 – 3x2 – 2y² at which the tangent plane is perpendicular to the…

A: Given, Surface, z=8-3x2-2y2 at which the tangent plane is perpendicular to the line…

Q: 7. Find the equation of the tangent plane to the surface: x +y² -z² 1 z, at (2, 1, 2)

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Q: Compute the integral |(5y + pz2020, ) dx + (19x – e-4ycos(v) sin y) dy over the portion of the…

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Q: Compute F. dr for the oriented curve specified. F(x, y, z) = (z³, yz, x), quarter of the circle of…

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Q: Verify the Green's theorem for the following integrol 3, Sinydx + + (x - cosyldy where curve C is…

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Q: 1) The plane of 2 = x*+y² X+y+2 = 12 and %3D inter sect along d para boloid Find the curve. lowest…

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Q: 4) The area of the surface generated by revolving x=y²-1, 1≤ y≤ 2 about x-axis is S=.

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Q: Find the equation of tangent plane to the surface z = ln (3x²) + 2y at A (1,0, In (3)).

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Q: Give arc-lengtu porametriz atian of the line which an Hhe tangent planes of and (1,2,9). is Hhe…

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Q: (#2) Find the area of the surface generated by revolving the curve about x-axis for f(x) = 2Vx on…

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Q: Calculate S. xydx + 3y*dy where C is the curve in xy plane, x = y² from (0,0). to (1,3).

A: We have to calculate the integral ∫Cxydx+3y4dy Where C is the curve in the xy plane, x=y2 from 0,0…

Q: 4 Determine the surface area of a funnel that is generated by revolving the graph of 1 y = f(x) =…

A: Given  y=fx=x3+112xand interval 1,2

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 2y3 dx…

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Q: 3. Set up the formulation to find the surface generated when the curve y = x² is revolved about the…

A: 1st we need to convert the curve in x=f(y) form and corresponding limits for y , Then use given…