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- Find parametric equations for the tangent line to the curve r(t) = < e^(-t)cos(t), e^(-t)sin(t), e^(-t) > at the point (1,0,1).Consider the parametric curve segment (t, t2), t ∈ [0, 1]. What is the firstorder derivative of the curve at t = 0? Show that exactly the same curve segment can be re-parameterized so that the first-order derivative at t = 0 is different.Find an equation of the tangent plane to the surface y ln xz2 = 2, at the given point (e, 2, 1) and find a set of symmetric equations for the normal line to the surface at the given point.
- Find an equation of the tangent(s) to the curve with parametric equations x = t cost, y = tsin t at the point corresponding to the parameter t = π.Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = 3 ln(t), y = 4t1/2, z = t3; (0, 4, 1)Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x=t^2+1, y=4(t^1/2), z=e^(t^2-t); (2,4,1)
- Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = sqrt(t2+15)y = ln(t2 + 15) z = t; (4, ln(16), 1) x(t), y(t), z(t)=?I am confused on how to find the parametric equations for the tangent line to the attached curve r(t) at the point (1,0,1)Find the 1st and 2nd derivatives of y with respect to x from parametric equations. a). x=3 (t + 2) 2 ; y = 9t2-5