Find T, N, and k for the space curves r(t) = (3sint)i + (3cost)j+ 4tk %3D

Q: Two particles travel along the space curves r,(t) = (t, t²,t³) and r2(t) (1+ 2t, 1 + 6t, 1+ 14t),

A: Given data: The first curve is r1(t)=<t, t2, t3>. The second curve is r2(t)=<1+2t, 1+6t,…

Q: Find the curvature k for the space curve r(t) = (4 +t)i + tj. %3D Lütfen birini seçin: a. 3/2 b. 2…

A: Given curve is Applying derivative: Applying derivative again:

Q: Consider the region enclosed by the curves y = r² + 1 and y = 2r + 1:

A: Consider the region bounded by the curves y=x2+1 and y=2x+1 The intersection between the curve is,…

Q: Find T, N, and k for the space curves r(t) = (t3/3)i + (t2/2)j, t > 0

A: Given, the space curve r(t) = (t3/3)i + (t2/2)j, t>0 We have to find the T, N, and K for this…

Q: Determine whether the space curve given by r(t) = (t, t 3 , t 2 + 1) intersects the xy-plane, and if…

A: Given the space curve,  r(t)=t,t3,t2+1

Q: the surface z = &x + 4y th=

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Q: Find T, N, and x for the space curve r(t) =7i+j,t>0. T(t) = (O i+ (O i

A: Formula for T, N and k are defined as  T=vv, where v=drdt N=dTdtdTdt and k=1vdTdt

Q: Find the Curvature of the space curve r (t) = t i + t? j + -2 t3 k at t = Enter an integer or a…

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Q: Find T, N, and k for the space curves in Exercise r(t) = (t3/3)i + (t2/2)j, t > 0

A: Given, r(t) = (t3/3)i + (t2/2)j, t > 0

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 the absolute minimum and maximum of f(x,y)=2x^3+y^4  over the disk x2+y2 ≤ 1

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Q: Find the shortest distance between the surface z = x² + y² and the plane r + y – z = 4.

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Q: Find the equation of the tangent plane to *+ y? at the point (2, –3, 10) the surface z = 4 O x + 4y…

A: We have to find

Q: Which of the following correctly represents the plane region in the first quadrant bounded by the…

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Q: If the infinite curve y = e-6x, x > 0, is rotated about the x-axis, find the area of the resulting…

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Q: If (a,B,y) is a point at which the surface x-+y²-z²-2x+12=0_has a horizontal tangent plane, then…

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Q: Find the absolute maximum and absolute minimum of f(x, y) = yx^2−y^2+4 on the unit disk  (x, y) :…

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Q: Find the minimum distance between origin and the plane 3x + 2y+z=14 O a. 2y2 O b. 3/2 O C. V14 O d.…

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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: Sketch the space curve r(t) = −ti + 4tj + 3tk and find its length over the given interval [0, 1] .

A: Given space curve is rt=-ti+4tj+3tk. Sketch the above space curve as shown below.

Q: If the infinite curve  y = e−4x, x ≥ 0,  is rotated about the x-axis, find the area of the…

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Q: Find T, N, and k for the space curve r(t) = i+Tj, t> 0. T(t) = (O i+ (Oi

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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: Which type of surface does the curve x=t2, y = tsin(t), z=tcos(t) lie on?

A:

Q: et T(x, y, z)= 100+ x² + y² represent the temperature at each point on the sphere x² + y² + z² = 80.…

A: Given: Tx,y,z=100+x2+y2sphere g= x2+y2+z2=80plane h =x-z=0

Q: Evaluate the integral [(3x – 2y + z)ds where C is the curve, C, and C, as shown. 3 y²+ z² 2 G 2* 3…

A: Given that ∫c3x-2y+zds. The objective is to find the integral value. ∫c3x-2y+zds=∫c13x-2y+z…

Q: Find the maximum and minimum values of a function F(x,y.z)3D8X+y+ z on the surface A

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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: Find the distance from a point P(x1, y1, Z1) to the plane Ax + By + Cz = D.

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Q: Find for the point P(x,y,z) on the plane 3x + y – z – 15 = 0 that is closest to the origin.

A: The distance of the point P(x,y,z) from the origin is: d2=x2+y2+z2 Now we have to minimize d if the…

Q: The tangent plane to the graph of the surface z=In(x2+y2) at the point (1,0,0) contains point…

A: Given function is, z=lnx2+y2

Q: Find the area of the band cut from the paraboloid x² + y² – z = 0 by the planes z = 2 and z = 6.…

A: Given equation is, x2+y2 = z Band cut from the given paraboloid by the planes z = 2; z = 6 Area of…

Q: Find the region in the xy-plane in which the following equation is hyperbolic: ((x- y)? - 1]u + 2u,…

A: Given partial differential equation x−y2−1uxx+2uxy+x−y2−1uyy=0 We have to find the region in the…

Q: 14. Under the paraboloid z=x² +y2 and above the disk x +y² <9 for (x,y) in the first quadrant.

A: we have to find the volume

Q: Q3/ Sketch the surface z 3x2 + y? +1 and find its linear approximation at P.(0,-1).

A:

Q: FIND B AND T FOR THE SPACE CURVES. r(t) = (6sin2t)i + (6cos2t)j + 5tk

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Q: Let R be the region enclosed by the loop of the t², y = t³ – 3t. parametric curve x =

A:

Q: Find the curvature of the space curve. r(t) = - 3i + (3+2t)j + (t +8)k %3D

A: The given curve    r(t)=-3i+3+2tj+t2+8k

Q: If (a,B,y) is a point at which the surface x²+y²-z²–2x+104=0 has a horizontal tangent plane, then…

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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 a generating curve on the xz-plane for the surface of revolution with equation x2+ y²+ z²= e2x…

A: The solution is given below

Q: Consider the following space curve r (t) = t²i + 2tj – v2 43/2 k %3D 3

A: The given space curve isrt=t2i^+2tj^-423t32k^.To find:The time period when rt intersects xt+zt=0 and…

Q: Find the absolute maximum and absolute minimum of f(x, y) = yx² – y² +4 on the unit disk {(x, y) :…

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Q: Find T, N, and k for the space curve r(t) =i+ i, t>0_

A: In this question, we find the unit tangent and unit normal along with the curvature of given r(t)

Q: Find the curvature K for the space curve r(t) = (/3sint)i + (sint)j+ (2cost)k.

A: Let, γ(t) be a space curve. The curvature of the space curve is given by, κ=γ'(t)×γ"(t)γ'(t)3.

Q: Let C be the boundary curve counterclockwise of the semidisk æ? + y? 0. Then fc(-2ydx + 3xdy) 5dydx…

A:

Q: Find the distance between the point P(1, 1, 1) and the surface x² + 2y² + 3x² = 1.

A: Given Point P1, 1, 1 and surface x2+2y2+3z2=1

Q: The tangent plane to the graph of the surface z=In(x<+y<) at the point (1,0,0) contains point…

A: and point (1,0,0)