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Find parametric equations for the tangent line to the curve with the given parametric equations at...

Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.

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Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.
3. (5 points) (a): Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.$$ x=e^{-t} \cos t, \quad y=e^{-t} \sin t, \quad z=e^{-t} ; \quad(1,0,1) $$(b): Find the unit tangent vector \(\mathbf{T}\), the principal unit normal \(\mathbf{N}\), and the curvature \(\kappa\) for the space curve,$$ \mathbf{r}(t)=<3 3="" 4="" sin="" cos="" t="">$$
Find a set of parametric equations for the tangent line to the curve of intersection of...
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Find a set of parametric equations for the tangent line to the curve of intersection of...
Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces at the given point. (Enter your answers as a comma-separated list of equations.) z = sqrt(x2 + y2) , 9x − 3y + 5z = 40, (3, 4, 5)
1. Given parametric equations below, find dy/dx , equations of the tangent and normal line at...
1. Given parametric equations below, find dy/dx , equations of the tangent and normal line at the given point. (a) x = t^2 , y = t^3−3t at t = 1 (b) x = cos(t), y = sin(2t) at t = π/4 2. ) Given parametric equations below, find d^2y/dx^2 and determine the intervals on which the graph of the curve is concave up or concave down. (a) x = t^2 , y = t^3−3t (b) x = cos(t), y...
Find the equation of the tangent plane and the parametric equations for the normal line to...
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1. Given parametric equations below, find the values of t where the the parametric curve has...
1. Given parametric equations below, find the values of t where the the parametric curve has a horizontal and vertical tangents. a) x=t^2 - t, y= t^2 + t b) x= e^(t/10)cos(t), y= e^(t/10)sin(t) 2. Find the arc length of the graph of the parametric equations on the given intervals. a) x= 4t+2, y = 1-3t , −1 ≤ t ≤ 1 b) x= e^(t/10)cos(t), y= e^(t/10)sin(t), 0 ≤ t ≤ 2π
Question: (a) Find parametric equations for the line of intersection of the planes given by 3x...
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Find the equation of the tangent line to the curve at the given point using implicit...
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Find the equation of the tangent line to the curve given by: x= t2 + 2t...
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