[15] 1. Consider the curve (t) = (12t, 8t3/2,3t2), with 0 < t < 1. Find its %3D velocity, acceleration and curvature at t =1 and evaluate the total length of the curve. thy oftrer

Q: ind the equation for the tangent plane to the surface z = In(6x2 +9y2 + 1) at the point (0,0, 0).…

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Q: (a) Find an equation of the tangent plane to the surface of z = ye(3ry-y²) at (-1, –3, –3). (b)…

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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: 35. Find the area of the surface generated by revolving the para- metric curve x =1, y = 2r² (0 <t s…

A: Given, x=t,y=t2,0≤t≤1 The area of the surface generated by revolving the parametric curve about the…

Q: ne if the curve (In t. t In t. 1) is tangent to the surface rz- uz? + cos Tu =1 at (0.0. 1).

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Q: Find the equation of the tangent plane to the surface 4xe^yz+xz^2−7x^3y= 5 at(1,0,1).

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Q: Find the point(s) on the surface z = 3 − x2 − y2 + 6y, at which the tangent plane is horizontal.

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Q: Find the length of the following three-dimensional curve r(t) = (9+3t,3 – 7t, – 1+ 5t) , for 1sts6…

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Q: Find equations for the horizontal and vertical A)y= at (1, 똥) B) z = 0 at (0, ) D) y = 2 at (2, *)…

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Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx2 + y2, (12,…

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Q: Find the exact length of the curve. y = In(sec(x)), Osxs n/4

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Q: Calculate the arc length of the curve f(x)=(2/3)(x²+1)ª2) in the interval [–1,1]

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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: Show that at any point (x,y) on the curve y=bex/a , the length of the subtangent is constant and the…

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Q: the detined b is Constant. Curiature a(t) =| 1 Cost, 1 sint, o of the curve d:laa)tR? where Find

A: We are given : α(t)=1rcos t,1rsin t,0 ⇒α'(t)=-1rsin t,1rcos t,0 Now, the Unit tangent Vector is :…

Q: Find an equation of the tangent plane to the surface at the given point z= 5x - xy3+y2,     (1,1,5)

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Q: Consider the curve parametrized by x www = 1 + ln(t) and y = t¹ + 2t. dy a) First eliminate the…

A: topic - derivatives

Q: Find the point(s) on the surface z = xy + 1/x + 1/y at which the tangent plane is horizontal.

A: Given that: The surface  z = xy+1x +1y  .

Q: Find the slope of the tangent line to the parametric curves x=3t+2, y= 2t^2+ 3t-3 at t=11 and then…

A: The given question as belonging to the derivative in which we have to find the derivative or the…

Q: Find a curve through the origin in the xy- plane whose length is given by 1/2 L = [; (1+ *)"* dx 4

A: The arc length, L of a curve y=f(x) in the interval a,b is calculated using the formula below.…

Q: Q:Find the that is POT HOh of the curve area of the suoface generated by revolving the Y=x² between…

A: Using area formula we have

Q: Find the equation of the plane tangent to the surface of Z= x2+ Y2 at point P(125)

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Q: For KEIRT and TEIR construct Co-Curve Y: IR→IR³ with constant Curvature K and constant torsion T

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Q: Find the equation of the tangent plane to the surface y = 2a2- z2 at the point (0,-1, 1)

A: Here is the solution

Q: At which of the points below is the tangent plane to the surface - 2y² + z²+ yz = 2 vertical? Select…

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Q: Find an equation of the plane tangent to the following surface at the given point. V3 A,1, sin (xyz)…

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

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Q: 35. Find the area of the surface generated by revolving the para- metric curve x =t, y = 21² (0 <…

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Q: Q2. A particle moving along the curve R(t)=(cost +1 sint)i + (sint -t cost)j,find acceleration…

A: Solution:

Q: Consider a χ2-curve with df = 16. Obtain the χ2-value that has area a. 0.025 to its left. b. 0.975…

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Q: The parametric curve x(t)=t−2t6 and y(t)=t7+2t2 is given. In which case is the tangent line at the…

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Q: Find the tangent plane to the graph of **yz +z'e* -y² = 5 at (1,3,2).

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Q: Find an equation of the tangent plane to the given surface at the specified point. f(x,y) =…

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Q: 9. Find an equation for the tangent plane and the normal line to the surface xy + yz + zx = 5 at the…

A: f(x,y,z)=xy+yz+zx-5=0,  at  (1,2,1)now we differentiate above equation with respect to x,y,z…

Q: Find an equation of the plane tangent to the following surface at the given points. z =6 cos (x- y)+…

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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: 1. Find the equation of the tangent plane to the surface cosh [exp (x²y)] = Z y? at the point where…

A: We will find out the required equation of tangent plane.

Q: Find the equation of the tangent plane to the surface x^2e^z+xyz+y= 3 at the point (1,2,0)

A: Find the equation of the tangent plane to the surface x^2e^z+xyz+y= 3 at the point (1,2,0)

Q: Find an equation of the tangent plane to the surface at the give h(x, y) = In √x² + y², (12, 16, In…

A: we have to find tangent plane

Q: Let r(t) = -6t2 î+ (t² +3) ĵ + 7 k for t > 1. Reparameterize in terms of the arc-length parameter.

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Q: 35. Find the area of the surface generated by revolving the para- metric curve x = t, y = 21² (0 < 1…

A: Given: x=t y=2t20≤t≤1

Q: 4. Find the equation of the tangent plane to the level surface x4 + yz – yz² + 5x = 0 at 3

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Q: Find the length of parametrized curve given by  x(t) = 6t2 + 12t, y(t) = -4t3- 12t2 - 9t where t…

A: Consider the parametric curve given by: x(t)=6t2+12t and y(t)=-4t3-12t2-9t for t from 0 to 1. The…

Q: s to the curve y = x* at the %3D

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Q: 10. Find the equation of the tangent plane to the surface z y ln x at (1, 4, 0)

A: Given Data : Surface z=yln(x) To Find: Equation of tangent to the surface at 1,4,0 For a surface S…

Q: 4. Find the area of the surface generated by revolving the given curve about the -axis. y = 7x,0 <…

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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: Find the angle of inclination of the tangent plane to the surface 3x2 + 2y2 − z = 15, at the given…

A: We have given surface 3x2+2y2-z=15 at point (2, 2, 5)   We have to find the angle of inclination…

Q: Find the length of the curve r(t) = for 0 ≤ t ≤ 2π Enter the exact value.

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