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- determine the parametric coordinate of the critical point of the curve x=t^2+3t=2 and y=t^2-1.1. If the parametric curve $x=f(t), y=g(t)$ satisfies $g^{\prime}(1)=0,$ then it has a horizontal tangent when $t=1$Consider the graph ofr(t) = 2t^2i + t^2j + t^3 kDetermine parametric equations of the tangent line to the curve at the point where the curve intersects the planex − 2y − z = 8.
- Find the 1st and 2nd derivatives of y with respect to x from parametric equations. a). x=3 (t + 2) 2 ; y = 9t2-5Show that y1(t) = cos(3t) and y2(t) = sin(3t) are linearly independent for all t.Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = t2 + 24 , y = ln(t2 + 24), z = t; (5, ln(25), 1)
- Find parametric equations for the tangent line to the curve of intersection of the paraboloid z = x2 + y2 and the ellipsoid 3x2 + 2y2 + 6z2 = 29 at the point (−1, 1, 2).Find the length of the parametric curve x = e^t + e^-t, y = 5-2t on the interval [0,3].Find the First and Second derivatives of y with respect to x from parametric equations. a). x=3 (t + 2) 2 ; y = 9t2-5
- Find a parametric description for the curve y=4-x^2 from (-2, 0) to (2, 0) such that t=0 corresponds to (-2, 0)find the location of a point xyz that satisfies the condition I) xy<0, z=3ii) |x|<2Consider 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.