V7x + 2y – x = y.

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

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Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 9x2 +…

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Q: (b) Investigate where the curve y = xy4 - x² is concave up and concave down?

A: Given curve is y=x4-x2 find the concavity of the given curve

Q: Sketch the plane curve r(t) = 2ti − 3tj,  and find its length over the given interval [0, 5]

A: Given plane curve: The parametric form of vector valued function is It is the equation of line in…

Q: Find the equation of the tangent plane to the surface determined by x^3y^2+z−35=0 where x=3 and y=5.

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Q: mine an equatio

A: Here we have to find the equation of rectifying plane to We have,

Q: Find the equation of the tangent plane at the point T(1,1,4) of the sphere (x – 1)2 + (y – 2)² + (z…

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Q: Sketch the plane curve r(t) = 3ti − tj and find its length over the given interval [0, 3] .

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Q: Find an equation for the set of points equidistant from the xy-plane and the yz-plane.

A: Find an equation for the set of points equidistant from the xy-plane and the yz-plane.

Q: Find the equation of the surface of revolution generated by revolving the curve z²=4y in the…

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Q: Evaluate SF dR given that F (x, y) = 2yî + (xy – 2x) %3D and C is the curve in the third quadrant…

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Q: Find the equation of the tangent plane to the surface z = at the point (2,-3, 10) O r- 6y – z = 10…

A: We have to find the equation of tangent plane.

Q: Find a point on the curve y = x² that is closest to the point (18, 0). %3D AY y =2 (x, y) (18, 0)

A: Find a point on the curve y=x2 that is closest to the point  Here use distance formula…

Q: Identify a generating curve on the xz-plane for the surface of revolution with equation x? + y? +z?…

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Q: Use Eq. (7) to find the point P nearest to Q = (2, 1, 2) on the planex + y + z = 1.

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Q: Find the equation of the tangent plane to the paraboloid z = 2x2 +y? at the point (1,2,6). Select…

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Q: Find a parametrization of the line in which the planes x+y +z= -2 and y +z= 6 intersect.

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Q: عنوان الدرس. / الموافق Find equation of the plane that cont the line s L,:X= Sty=Ct 6+2t .....…

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Q: Find an equation of the tangent plane to the surface z = 2a2 + 1y – la – 3y – 1 at the point (5, 3,…

A: Equation of Tangent Plane to the surface F(x, y, z) = 0 at point (x0, y0, z0) is given by ∇F(x0, y0,…

Q: Sketch the surface given by the function. z = 9-x?-y?

A: Given, z=9-x2-y2

Q: (b) Find the point that makes the tangent plane to the surface z = x² – xy + y? – 2x + 4y…

A: Find the partial derivatives with respect to x and y and set equal to zero. Solve for x in the…

Q: Find the point closest to the origin on the curve of intersection of the plane x + y + z = 1 and the…

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Q: Identify a generating curve on the XZ-plane for the surface of revolution with equation x? + y2 + z?…

A: Given: Surface of revolution with the equation x2+y2+z2=e2x To find: Identify a generating curve on…

Q: find the distance from the point to the plane. (1, 0, -1), -4x + y + z = 4

A: Concept -Let the equation of plane be -Ax+By+Cz+D = 0And the coordinates of a point be - (x1, y1,…

Q: Find the equation for the tangent plane to the surface z = - 9x - 7y at the point (2, 1, - 43). O A.…

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Q: Calculate a 3 ydz t 13x'y dy, Where Cis the oriented curve given in the figure . 3 Bydr+43xy dy =?…

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Q: Compute the length of the curve given parametrically by x=1/3t^3 and y=1/2t^2 for 0 less or equal to…

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Q: Find the length of the parametric y = 2 , - V3sts V3. curve x = 1+

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Q: 6y dA, R is the quarter-disk in the fourth quadrant enclosed by the curves r+ y = 16, r = =0, and y…

A: Explanation of the answer is as follows

Q: Find a parametrization for the line through the point (a, b) having slope m.

A: Given that slope = m , this can be written as <1,m> vector. And point= (a,b)

Q: Sketch the section of the surface at y=0. z = /2+x² + y?

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Q: Find the areas of the surfaces generated by revolving the curve x= 2sqrt(4-y), 0≤y≤15/4

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Q: Determine the length of the parametric curve given by r = 2t3, y = 3t² where 0 <t<V8. %3D CS Scanned…

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Q: At what point on the curve x = t³, y = 6t, z = t4 is the normal plane parallel to the plane 6x + 12y…

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Q: Find the curvature of the plane curve y = -t at the point t = 2. к(2) -

A: Given:y = -t4differentiating with respect to t, we get:            y' =     d(-t4)dt…

Q: Find the point at which the line F (t) = +t intersects the yz plane.

A: Given: An equation of a line in the parametric form is, r→t=&lt;2,-7,7&gt;+t&lt;-5,-6,6&gt; The…

Q: Find the point at which the line 7(t) = +t intersects the yz plane.

A:

Q: Identify a generating curve on the XZ-plane for the surface of revolution with equation x? + y2 + Z?…

A: Solution-

Q: 9) Sketch x = indieate the onientatiba of the 2t°, y = 3t, -4sts4 aud with %3D Curve an arow,

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Q: Find the distance between the point and the plane. (0, 0, 0) 2x + 6y + z = 12

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Q: Find rectifying plane of et, é, t at the curve t%3DL

A: Given curve is αt=et,e-t,2t.  To find the rectifying plane of the curve . Result: Let rt→=xt,yt,zt…

Q: (b) Find the point that makes the tangent plane to the surface z = x- xy +y-2x + 4y horizontal.

A:

Q: Find an equation for the surface of revolution formed by revolving the curve z2 = 2y in the yz-plane…

A: To find the equation for the surface of revolution

Q: Find the equation of the tangent plane at the point (-2,1 – 3) to the ellipsoid surface + y? + = 3.

A: Find the equations of the tangent plane and normal line at the point (-2, 1, -3) to the ellipsoid…

Q: Find the curvature of the plane curve y = 4t³ at the point t = 2.

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Q: Find the equation of the tangent plane to the surface determined by a'y + z- 55 = 0 at a = 4, y = 3.…

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Q: What is the maximum height of a particle whose path has parametric equations x = t9, y = 4 − t2?

A: The height of the particle is given by it's y position: y = 4 - t2 At the maximum height, dy/dt = 0

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: Sketch the plane curve r(t) = t2i + 2tk, and find its length over the given interval [0, 3]

A: We have, r(t)=t2i+2tk  we have to determine the length of the curve over the interval [0,3]