Find T, N, and k for the space curve r(t) = - ti - (a cosh (t/a))j, a > 0.

Q: Sketch the space curve and find its length over the given interval r(t) = ⟨8 cos t, 8 sin t, t⟩,…

A: Given Finding the derivative with respect to t:

Q: Find an equation for the tangent plane to the surface z+1 = ry* cos(z) at the point (1, 1, 0)

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Q: Let y be the curve with vector form r(t) = (1/(t+ 2), sin(sin(sin t)), e-"). a) Determine whether…

A: The parametric curve is r(t)=⟨1t+2, sin( sin( sin t)),e-t⟩. x(t)=1t+2, y(t)=sin( sin( sin t)),…

Q: find the tangent plane to the surface z = Vy-x at the point (1,2,1)

A: Equation of tangent plane is z-c = df/dx(x-a)+df/dy(y-b) at point (a,b,c)

Q: Find an equation of the tangent plane to the given surface z = x sin(x + y) at the point (-1, 1, 0).

A: Given,  z=x sin(x+y) ⇒x sin(x+y)-z=0 Let f(x,y,z)=x sin(x+y)-z Recall: The equation of the tangent…

Q: Find equation of the plane tangent to the following surface at the given point. an z = tan(xy):…

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Q: Find the point on the surface z=x2-y2 at which the tangent plane is parallel to the plane…

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Q: Find an equation of the tangent plane to the surface at the given point. z = x2 - 2xy + y2,  (2, 3,…

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Q: Find T, N, and k for the space curve r(t) = - 2e cos t)i- (2e sin t) j+ 2k.

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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, (6,…

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Q: Given: vector-valued function R(t) whose derivative R'(t) = (4t, 6t, —12t) (c) Determine the…

A: Here is the solution of the given problem.  To solve this problem we use simple concept of…

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 point(s) on the surface z = 5xy, at which the tangent plane is horizontal.

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Q: Given: vector-valued function R(t) whose derivative R'(t) = (4t, 6t, —12t) (b) Reparametrize R using…

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Q: Sketch the space curve r(t) = ⟨2 sin t, 5t, 2 cos t⟩ and find its length over the given interval [0,…

A: The given equation of space curve is  r(t) = ⟨2 sin t, 5t, 2 cos t⟩.

Q: Sketch the space curve r(t) = i + t2j + t3k and find its length over the given interval [0, 2] .

A: If r=x(t)i+y(t)j+z(t)k then length of r over [a, b] is L=∫ab[x'(t)]2+[y'(t)]2+[z'(t)]2dt

Q: Find an equation for the tangent plane to the surface f(x, y) = e^xy + 4x^2 + 4y^2 at the point…

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Q: Find T, N, and k for the space curves r(t) = (cosh t)i - (sinh t)j + tk

A: Let the given space curve is r(t)=(cosh t)i-(sinh t)j+tk   To determine: The values of the unit…

Q: Find an equation of the tangent plane to the surface x = u² + 1, y = v³ + 1, z = u + v at the point…

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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,…

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Q: 2. Let L be the line tangent to the space curve represented by r(t) = (t² – In(t))i+(e²-t – t)j+…

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Q: Find the tangent plane for the level surface f(x,y,z) = 3x5 + cos (5y) + In (5z) = c at the point…

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Q: H.W: find the tangent plane to the surface z = Vy -x at the point (1,2,1)

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Q: Evaluate F. dī where F = , and C' is the circle of - counterclockwise direction.

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Q: Sketch the space curve r(t) = a cos ti + a sin tj + btk and find its length over the given interval…

A: Given : Space curve equation rt = acosti^ + asintj^ + btk^  ,   and  t ∈ 0,2π  ,a and b are contants…

Q: Find the equation for the Tangent Plane on the given surface coS ax – x²y + e*z+ yz = 4 Po(0, 1, 2)

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Q: Let C be the space curve r(t) = (3 sin(t) – 1,4 sin(t) + 1), 0 < t < . The length of C is

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Q: 4. Let f(x, y) = sin(x²y) + vx + e+y. Find the equation of the tangent plane to the surface z f(x,…

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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, (3,…

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Q: 3. Sketch the space curve, r(t) = 8 cos ti +8 sin t j+tk , and find its length over the interval []…

A: Given: r(t)=8cost+8sint+tk    [0,pi/2]

Q: Find the tangent plane to the following surfaces at the point (1, 2, 3): a.) z = x + y     b.) z + 2…

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Q: Find an equation of the plane tangent to the following surface at the given point. z = tan'(xy);…

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Q: Find the tangent plane for the level surface f(x,y,z) = 7x5 + cos (5y) + In (9z) = c at the point…

A: Answer: In oerder to use gradients we introduce a new variable c= 7x5+cos(5y)+ln(9z) Therefore the…

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

A: We have to find the equation of tangent plane

Q: Evaluate F-di where F(x, y, z)=1li +(x+yz)j+(xy- Vz 3x+2y+z=6 in the first octant. C is a positively…

A: Here we have to evaluate ∫CF→·dr→=? Where F→(x,y,z)=i^+(x+yz)j^+(xy-z)k^ and C is the boundary of…

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 equation for the tangent plane to the surface z = x2 at the point P (1,1,1). Select the…

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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: Find the tangent plane to the elliptic paraboloid z = x² – 2y at the point (1,1,1). - O A. z = 2x –…

A: Given that: z=x2-2y2      and point is:   (1, 1, 1)

Q: Let F(x, y) = -z|. Let C be the curve parametrized by (t, cos(t), sin(t)), where 0 <t<. y Evaluate:…

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Q: Sketch the space curve r(t) = ⟨4t, −cos t, sin t⟩ and find its length over the given interval [0,…

A: Consider the given space curve, rt=4t,-cost,sint use the graphing utility to graph the curve,

Q: Find an equation of the tangent plane to the given surface at the specified point. z = y In(x), (1,…

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Q: Find the point on the graph of z = (x² + y)? at which the tangent plane is parallel to the plane 2x…

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Q: Find an equation of the tangent plane to the given surface at the specified point. z= e(x^2)-y2,…

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Q: Let C be the curve in the plane with parametrization r(t) = cos ti+ sin tj for t e [0, 4T]. Compute…

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Q: 2. Find the parametrization of the tangent line to the space curve r(t) = (-t3, In(t), e² ) at t =…

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Q: Given: vector-valued function R(t) whose derivative R' (t) = (4t, 6t, -12t) (b) Reparametrize R…

A: Let's reparameterize vector value function R(t).

Q: Find an equation of the tangent plane to the given surface at the specified point. z = V xy, (2, 2,…

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