At an air show, a jet has a trajectory following the curve y = x2. Ifwhen the jet is at the point (1, 1), it has a speed of 500 km/h, determineits tangent vector at this point.

Q: What is the unit tangent vector to the curve r(r)=sint i+2cost j when t=π/4

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Q: Find the equation of the tangent plane to z = f(x, y) at the point (1, , 1).

A: Given Data: Surface: z=x2esiny Point: x0, y0, z0=1, π, 1   (a) The first derivative of the given…

Q: Find the tangent plane to the equation z = 6e* – 2y at the point (4,8,6) - II

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Q: .3 At which point P does the curve r(t) = ( 2t have the tangent vector (24, -8, 3) ? (a) P(2, 2, 2)…

A: Here we have, the given curve is r→(t)=2t3, 2t2, 3t-1                now differentiate with respect…

Q: Find the tangential and normal components of acceleration for a projectile fired at an angle 0 with…

A: we know that for projectile fired at angle θ with the horizontal tangentialTt and normalNt…

Q: Consider the curve y = 10 + 4x − x^(2) at (x, y) = (3, 13). Find a vector, v, that has length 4 and…

A: Given the curve y=10+4x-x2 at (x,y)=(3,13).

Q: find acceleration Components of the point moving the Curve on + t"k at

A: Since you have posted multiple questions, but according to guidelines, we will solve first question…

Q: Find an equation of the tangent plane and a normal line to the surface z = In Vx2 + y2 at the point…

A: Given that: z=lnx2+y2

Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t): = 7 cos(t)i…

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Q: Find for the equations for tangent plane and normal line at P,on the given surface 2 х2 — 3ху —у? -2…

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Q: Find a parametrization of the tangent line at the point indicated. r(t) =〈4t, 5t, 9t〉,t = −4

A: To Find a parametrization of the tangent line at the point indicated. r(t) =〈4t, 5t, 9t〉,t = −4

Q: Find the equation of the tangent plane to the surface - 8x3 + 7y³ + 3xy at the point (2,0, 64).

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Q: Sketch the curve parametrized by r(f) = (1 – 12, 1) for -1sı<1. Compute the tangent vector at i = 1…

A: Let's first draw the curve -  Domain - -1 ≤ t ≤ 1 where, we can take values of t as -  t = -1, -0.5,…

Q: Find the tangent plane to the equation z = - 32² – y² + 3y at the point ( – 5, 3, – 75)

A: z=-3x2-y2+3y  and the point (-5,3,-75)

Q: Find the unit tangent vector for the parameterized curve: r(t) = 2ti + 2cos tj - 2 sint k

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Q: Find the vector equation of the tangent line to F(t) = (2 sin 2t, cos 2t, – 6t) at the point where…

A: Consider the given vector. rt=2sint,cos2t,-6t   Find the derivative of the vector with respect to t.…

Q: Find a vector equation of the tangent line of f(t) = (cost, sint, t) at the point Po (0, 1,

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Q: Find the unit tangent vector of the curve: 7(t) = (3 cos t , 3 sint, t2) at t = 0. %3D

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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: Find the tangential and normal components of the acceleration vector for the curve 7(t) = (- 3t,…

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Q: Find the tangent plane to the equation z = 2x – 3y + y at the point (1, 2, – 8). -

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Q: Find an equation of the tangent plane to the surface at the given point.   z= y/1+6x…

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Q: Find the tangent line(s) to the parametric curve given by a = t5 – 4t3 y = t? at (0, 4).

A: Find the tangent line(s) to the parametric curve given by x = t^5-4t^3 , y = t^2 at (0,4).

Q: Find parametric equations for the tangent line to the curve a-tcost, y-t, z- tsint at the

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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: Find the equation of the tangent plane to z = e® +y+y +1 at the point (0, 2, 12). 2 =

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Q: Find a vector equation for the tangent line to the curve 7(t) = (5 cos(6t)) i + (5 sin(6t)) j+…

A: Given the vector function, r(t), we call r′(t) the tangent vector provided it exists and provided…

Q: Find the point on the graph of z = 3x2 – 2y? at which vector n = (-12, –16, –2) is normal to the…

A: Shown below

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

A: We find out dy/dx .then we find out value of t at given points and then find slope of tangent line…

Q: Find the tangent plane to the equation z 5a2 - 4y +5y at the point (5, 5, - 200)

A: The equation of the tangent plane to a surface  is given by fx(x-a)+fy(y-b)+fz(z-c)=0where (a,b,c) =…

Q: Find an equation of the tangent plane to the surface at the given point. z = 5 - 2x - y, (3,-1, 1)

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Q: for the follawing , find the unit tangent vector: parameterized curve rit) =<2 sint) , 2 cos lt),5…

A: Given: r(t)=2sin(t),  2cos(t), 5cos(t),  0≤t≤π The unit tangent vector to curve r(t) is…

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: Find an equation of the tangent plane to: 3x +y = z at P(-1,1,-2) %3D

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Q: Find the equation of the plane tangent Z = (x+2)*- (y-1)²-5 at (2,3,3) to

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Q: Obtain the gradient to a curve with the parametric equations given by I = In - and y = sinh 2t whent…

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Q: Find the tangent line(s) to the parametric curve given by a = t¹ - 9t² and y=t² at (0, 9).

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Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In√√x² + y2, (3,…

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Q: The vector parametric form of the tangent line to r(t) = (3t², ¿, t – 1) at t = -5 is

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Q: Find the unit tangent vector to the curve defined by =(- 4t, 4t, V49 - t) at t = - 6. T(- 6)

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Q: Find an equation of the tangent(s) to the curve with paramnetric equations ¤ = 1+ VE, y = e" at the…

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Q: Find an equation of the tangent plane to the surface at the given point. fx, у) %3 х2 - 2ху + у2,…

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Q: ind an equation for the tangent plane of z = –2x²y – 3x² + y at the point (1, –1, –2).

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Q: Find the parametric equations of the tangent line to the curve represented by the vector function 7…

A: Topic  = Vector

Q: Find the equation of the tangent plane to the surface -2² at the point y = 2x2 – (0, –1,2)

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Q: (B) At point (1,5), Find the Vector that is tangent and Normal to the curve: X' = 2y + 10

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Q: x = 1+ vt, y = et X =1+1 Y. %3D

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Q: In R', Find the unit vectors that are parallel to the tangent line to the curve y = 2 sin x at the…

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Q: Find the tangent plane and normal line equations to x+y +z =1 at the point (1, %3D -2, -4).

A: This question is related to 3D geometry and equations of plane and lines,  we will solve it using…