List all of the points (x,y on the parcmetric curve X= +?+ 4+ y= 6+3 where the tangent line is pearallel to the line parametric equations; with X= -7+, y= 12+-5

Q: List all of the points (x, y) on the parametric curve t° + 4t, y = 6t? where the tangent line is…

A: Given that, Parametric equation of the curve are following, x = t3 + 4t,      y = 6t2 and the…

Q: Find the equation of the tangent plane to the surface y = 2x2 - z at the point %3D (0, -1,-2) y+2z =…

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Q: Find the length of one arc of the curve whose parametric equation are x=2θ-2sinθ and y=2-2cosθ.

A: We have to find length of arc whose parametric equations are : x=2θ-2sinθ and y=2-2cosθ Suppose 0 ≤…

Q: Find an equation for the tangent plane to the surface 22 – xy? = 0 at the point (1, 3, 3).

A: Given that At point (1,3,3) Take, Now to find the divergence of f, The divergence at point…

Q: Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces…

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Q: Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces…

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Q: Find the equation of the tangent plane to the following surface at the given point. 4y cos (3ar 2)…

A: Given equation of surface and point is

Q: Find the parametric equation for a line that is tangent (intersection) of the two fields below: −2x…

A: We have to find parametric equation for a line that is tangent (intersection) of the two fields…

Q: Find parametric equations of the tangent line to the curve of intersection of paraboloid z = x² + y²…

A: We know that tangent line to ellipse will be perpendicular to normal of both the surface. Therefore,…

Q: Find all equations of the tangent line to the common curve of the two surfaces with equations z = x²…

A: follow next step

Q: Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces…

A: Given surfaces are And the given point P is

Q: Find parametric equations of the tangent line to the curve of intersectic paraboloid z = x² +y? and…

A:

Q: Find an equation of the tangent plane to the surface z = -2z² – 2y?- lz 2y+ 3 at the point (5, 1,…

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Q: Determine the x - y coordinates of the points where the parametric equation x = 3 sint y = 3 cost 0≤…

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Q: 2. Find the equation of the tangent plane to the surface z = 3++ at point (-4, 3).

A: Topic- application of derivatives  Tangent to surface

Q: Find the equation of the tangent plane to the surface y = 2x2 - z2 at the point (0, –1, –1) %3D | |

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Q: Find the equations of the tangent lines to the curve whose parametric equations are x = 2t2 - 4t +…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Find the distance between the point (1, −2, 4) and the line given by the set of parametric equations…

A: The given point is M=(1, −2, 4) The direction vector of the line is =s=(2,1,2) A point on the line…

Q: Find an equation of the tangent plane to the surface 9x2 + y2 + 4z2 = 25, at the given point (0, −3,…

A: Concept: The two expressions connected by equal to be called an equation. The expression on the two…

Q: Find the equation of the tangent line to the common curve of the two surfaces with equations z = x²…

A: Please check step 2 for solution.

Q: Determine the x - y coordinates of the points where the parametric equation x = 3 sint y = 3 cost…

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Q: Find the length of arc of the curve given by the parametric equations x = t°, y=t² from the point…

A: Arc length is given byL=∫abdxdt2+dydt2dt

Q: Determine the parametric equation for a line that is tangent (intersection) of the two fields below:…

A: We have to find out parametric equation for a line that is tangent (intersection)of the two fields…

Q: Find parametric equations of the normal line to the surface z = + y? at the point (2, -2,5) x = 2 -…

A: Let F(x,y,z) define a surface that is differentiable at (x0,y0,z0) then the normal line to F(x,y,z)…

Q: equations

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Q: Sketch the curve with parametric equationsx = 3t − 4, y = 3 + t^3

A: Here we have to sketch the curve with parametric equations.  x=3t-4; y=3+t3

Q: Find parametric equations for the line tangent to the curves of intersection of the surfaces xyz =1…

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Q: Eliminate the parameter in the parametric equations x = 7+ sint, y = 2+ sint, for 0sts, and describe…

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Q: Find an equation for the tangent plane to z-x-y = 3 at the point (2, 1, 8) Z - ) %3D

A: given z-x2-y2=3 at point 2,1,8

Q: For which values of t is the parametric curve x=8t, y=t+t, -0c0s ts 00 concave up? (Enter your…

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Q: Find the tangent line(s) to the parametric curve given by a = t-9t and y =t at (0, 9) %3D %3D

A: We have to find the tangent line

Q: Sketch the parametric curve at R* whose parameterization is given by a (t) = (cos (t), sin (1), t),…

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Q: Find the distance from the point (3, 2, 5)to the line with parametric equations x=t,y =l +t ,z = 2 +…

A: The equation of the line in matrix form:                                                xyz = 012 +…

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: Find parametric equations of the line containing the .point (2, 3,-1) and normal to the plane x+…

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Q: Find parametric equations for the path of a particle that moves along the curve y=x from (1, 1) to…

A: Given Parabola is y = x²

Q: 9. Find the exact length of the parametric curve for the given interval. x = 4t 2 - 3, y = 3t, 0 St5…

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Q: Find an equation for the tangent plane to the surface x = u² – v², y = u + v, 2 = u² + 4v at (-},2).

A: We have r(u,v) = (u2-v2)i + (u+v)j + (u2+4v)k

Q: Find parametric equations for the line pass- ng through the point P(1, –1, 3) and perpen- licular to…

A: Given that: Line is passing through P(1,-1,3) and perpendicular to the plane:       4x+3y-2z=6.

Q: Find a parametric description for the curve x=y^2-9 from (0, 3) to (-5, -2) such that t=0…

A: We need to parametrize the curve x=y2-9 from 0,3 to -5,2 We need to put either x=t or y=t and see a…

Q: Find the length of the curve having a parametric equation of x= 2cos³0 and y=2sin²0 from 0-0 to…

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Q: Find the equations of the tangent plane and normal line to the surface with equation 9y? + 9z2 = 22…

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Q: Find set of parametric equations for the tangent line to the curve of intersection of the surfaces…

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Q: 5. Sketch the parametric curve x = t2 – t, y = t³ – 3t and determine the location (x, y and t) where…

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Find an equation of the tangent plane to the given surface at the specified point. 5Vy Z = (-1, 1,…

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Q: Draw the curve given by the parametric equationsx=t3+t2−t,y=t3+2t2−4t.

A:

Q: 2. Find an equation of the tangent plane to the parametric surface F(u, v) = (, 2uv, uv?) at the…

A: (2) Consider the provided question,

Q: Let C be the parametric curve defined by Ja(t)=1²-t-6, [y(t) = 41³ + 3t² - 6t. Determine the point/s…

A: a) Given that: xt=t2-t-6yt=4t3+3t2-6t For a horizontal tangent line, the slope must be 0. That…

Q: Find an equation of the tangent plane to the surface at the given point. - . z = 8 —х — у, 3 (3, –4,…

A: Given plane is z=8−83x−y. We have to find the equation of tangent plane to the surface at the point…

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.