x - y :(1, 2 - (2. –1. and x² + y?*

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

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Q: Curves on surfaces Verify that the curve r(t) lies on the given surface. Give the name of the…

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Q: Length of a curve Find the length of the curve --[Vvi-18 VVi - 1 dt, 1<x< 16.

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Q: Tangent Line Find the equation(s) of the tangent line(s) to the graph of the parabola y = x² through…

A: Given the parabola y=x2 (a) We have the equation of the tangent line with the slope m to the given…

Q: Parametric descriptions Give a parametric description of the form r(u, v) = ⟨x(u, v), y(u, v), z(u,…

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Q: Distance between two points A and B is 4 unit. Both A and B are lying same side of a variable line L…

A: Given that, distance between two points A and B is 4 unit. if you call θ the angle ∠LAB then you…

Q: Parametric equations and a value for the parameter t are given x = t2 + 1, y = 5 - t3; t = 2. Find…

A: For t=2, x=t2+1=22+1=4+1=5For t=2, y=5-t3=5-23=5-8=-3

Q: Tangent lines Find an equation of the line tangent to the cycloidx = t - sin t, y = 1 - cos t at the…

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Q: Normal Vector and Tangent Plane Find an equation of the tangent plane to the surface 4x2+ 9y2 - z2 =…

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Q: Parametric equations and a value for the parameter t are given x = t2 + 3, y = 6 - t3; t = 2. Find…

A: For t=2, x=t2+3=22+3=4+3=7 For t=2, y=6-t3=6-23=6-8=-2

Q: Part I: PARAMETRIC EQUATIONS. Find the second derivative of y with respect to x from the parametric…

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Q: Parametric equations and a value for the parameter t are given x = (80cos 45°)t, y = 6 + (80sin…

A: For t=2,  x = (80cos 45°)t = (80cos 45°)(2)= 80×22×2=802For t=2, y = 6 + (80sin 45°)t - 16t2= 6 +…

Q: NORMAL TANGENT AND STRAIGHT PLAN   Determine the equations of the tangent plane and parametric…

A: Given, z =xe-y⇒z-xe-y=0⇒F(x, y, z)=z-xe-y,we have to find the tangent plane and parametric equation…

Q: Tangent planes Find an equation of the plane tangent to the following surfaces at the given points…

A: Known fact: Let F(x,y,z) be the surface which is differentiable at P(x0, y0, z0). then the equation…

Q: Arc Length of a Plane Curve Find the length of the arc of the curve 8y = x4 + 2x−2 from the point…

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Q: Tangent planes Find an equation of the plane tangent to the following surfaces at the given points…

A: Find an equation of the plane tangent to the following surfaces at the given points (two planes and…

Q: Application

A: We will find the area with the largest dimensions.

Q: PARAMETRIC EQUATIONS. Find the second derivative of y with respect to x from the parametric…

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Q: Tangent lines Assume f and g are differentiable on their domains with h(x) = Ag(x)). Suppose the…

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Q: 5. x-1-1 ,y-6-2+름

A: Given: x = 1-1t,  y = 6 -7t +2t2 To find: The second derivative of y with respect to x from the…

Q: Tangent Lines and Intercepts Let L be any tangent line to the curve Vx + Jy = Jc. Show that the sum…

A: Given: x+y=c

Q: 4. x = V1 - t, y = t3 - 3t

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Q: Parametric descriptions Give a parametric description of the form r(u, v) = ⟨x(u, v), y(u, v), z(u,…

A: Given:

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

A: To find the parametric equations for the line tangent to the curve of the intersecion the surfaces,…

Q: Find parametric equations tor the tangent line to the curve with the given parametric equations at…

A: 29. Given,                  x=t,     y=e-t,    z=2t-t2;       (0,1,0)

Q: Find parametric equations for the line. (Use the parameter t.) The line through the points (0,, 1)…

A: Parametric equation of line with parameter t . x( t ) = x0 + a t y ( t ) = y0 + b t z ( t ) = z0 +…

Q: 1. 9y = x² ,0< x< 2 : х-ахis

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Q: Parametric descriptions Give a parametric description of the form r(u, v) = ⟨x(u, v), y(u, v), z(u,…

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Q: Intersection curve Find the curve r(t) where the following surface intersect. z = x2 - 5y2; z = 10x2…

A: To find the curve r(t) where the following surface intersect. z = x2 - 5y2; z = 10x2 + 4y2 - 36

Q: A. Direction: Find the equation of the tangent line of the following functions at the specified…

A: As per our guideline we supposed to answer only first question with  3 subparts slope of the tangent…

Q: 6. x = t2 - 3t + 4,y = t² + 4t – 5 7. x= 3+ 4 sine , y = 3cos0 – 4

A: The given equations are; 6)   x = t2 - 3t + 4.  , y= t2+4t-5 7) x=3+4sin(theta) , y= 3cos(theta)-4

Q: PARAMETRIC EQUATIONS. Find the second derivative of y with respect to x from the parametric…

A: dy/dx=(dy/dt)/(dx/dt)

Q: 12 The sketch shows the graph of y= Jx-1. -1 (i) Differentiate y = Vx - 1. (ii) Find the coordinates…

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Q: functions of several variables: so far I have Cylindrical, Quadratic, Sphere,  Can you name two…

A: Here we have to name the surface other than Cylindrical, Quadratic, Sphere.

Q: Part I: PARAMETRIC EQUATIONS. Find the second derivative of y with respect to x from the parametric…

A: This is a problem of application of calculus.

Q: Equation of Curve Coordinate Plane Axis of Revolution 33. y = 8z yz-plane z-axis %3D

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Q: Tangent planes Find an equation of the plane tangent to the following surfaces at the given point.

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Q: Find parametric equations for the line. (Use the parameter t.) The line through the points (0, , 1)…

A: The points through which the given line passes are,

Q: PARAMETRIC EQUATIONS. Find the second derivative of y with respect to x from the parametric…

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Q: Arc length of a parabola Find the length of the curve y = ax2 from x = 0 to x = 10, where a &gt;0 is…

A: Arc length of a curve is defined as the distance between two points along the section of the curve.…

Q: AREA OF A REGION 26 Find the area of the region bounded by, a. The curve y= 2/x ,x-axis, the lines…

A: The graph is shown below:

Q: 3. x = , y = t² – 4t + 1 4. x = v1 -t, y= t³ – 3t 1-,y=6-+ y = 6- 2+ t't2 2

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Q: Tangent lines Determine an equation of the line tangent to thegraph of

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Q: 1. x=1+t ,y= 4t – 3

A: Second derivative of the function y with respect to x is d^2 y/dx^2 = -8 / (3+y)^2

Q: Tangent lines Find an equation of the line tangent to thefollowing curves at the given point.

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Relationship between r and r' Consider the parabola r(t) = ⟨at2 + 1, t⟩, for - ∞ &lt; t &lt; ∞,…

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Q: estion 3 i) Find all points on the curve x(x + y²) = y where the tangent line is parallel to the…

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Q: Tangent planes Find an equation of the plane tangent to the following surfaces at the given points.

A: An equation of the tangent line to the surface F(x,y,z)=0 at point a,b,c is:…

Q: Tangent planes Find an equation of the plane tangent to the following surfaces at the given points…

A: Given:             z=2cos(x−y)+2;  π6,−π6,3 and π3,π3,4.

Q: quation of the tangent plane to the surface at the given point. y + z2 = 9, (1, 2, 2) of symmetric…

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