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A: We are authorized to solve only 1 question, please repost remaining questions Equation of tangent to…
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A: on solving this we get
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A: Find the length of the parametric curve x = e^t + e^-t, y = 5-2t on the interval [0,3].
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- 1. If the parametric curve $x=f(t), y=g(t)$ satisfies $g^{\prime}(1)=0,$ then it has a horizontal tangent when $t=1$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)computes curve length for 0<=t<=1 if r(t)=<sin 2t,2t^3/2,cos 2t>
- 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 the parametric equation for a line that is tangent (intersection) of the two fields below: −2x + 3y + 7z = −2 and x + 2y - 3z = −5Consider 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.
- 2 Calculate the (d^n*y)/(dx^n) derivative of the curve with the parametric equation x=lnt, y=t^alphaWrite the parametric equations for the tangent line to the curve of intersection of surfaces x=10x^2+2y^2 and z=x+y+10 at the point (1,1,12)Show that the curve = Vti + vt + (2t - 1) k is tangent to the surface x² + y2 -z = 1 when t = 1
- The velocity of a particle moving in the xy plane is given by the parametric equations dx/dt= -2^(t)sin(2^t) and dy/dt=2^tcos(2^t) for time t>=0. What is the speed of the particle when t = 2.3?30. If E 200 cosh 2x sin 2y a,+ 200 sinh 2x cos 2y a, V/m, find the equation of the di- rection line passing through the point P(1,0,0) and sketch it in the z-0 plane for 0 < x < 5 and 0 < y < /4.A particle moves in the xy-plane in such a way that its path is defined by x = e^t cos t and y = e^t sin 2t. Find the speed of the particle when t = /2.