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Q: 2. Consider the parametric curve r = t + 1, y = t - t. dy (a) Find d.r dy (b) Find da?
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Q: A curve is defined as the parametric equations: 1 x = acose, y=-asin 0, 0<0< 2n dy where a is a…
A: on solving this we get
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Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…
A: Given:
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Q: Find the length of the parametric curve C = {(x(t),y(t)) : t E I} x(t) = cos (t) , y(t) = sin³ (t),…
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A: The solution for the above problem is shown below.
Q: 1. For the parametric equations: x = 4t3, y= 2 +60t – 8t?, find: a) All values of t at which the…
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Q: consider the parametric curve x=t2 , y=9t-t3 . find dy/dx at t=2.
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A: Topic:- application of derivatives
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Q: Find the length of the parametric curve x = e^t + e^-t, y = 5-2t on the interval [0,3]
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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A: First differentiate x and y wrt t then divide
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Q: Find the length of the parametric curve I = cos(t) y = 1 + sin(t) from t = 0 to t =
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Q: Find an equation of the tangent line of the parametric curve, I = 1+÷, y=t³ –t² +3,
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Q: 2. Find parametric equations for the tangent line to the curve r(t) = (t8,t³,t7) at (1,1,1).
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Q: A curve is defined by the parametric equations T = sin t, y = 1 – cos t, 0<t< 27.
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Q: A curve is defined by the parametric equations: x(t) = e' cost, y(t) = e' sint dy d²y Determine and…
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Q: 1. Sketch the parametric curve x = (cos t) (1+ cos t), y= (sin t) (1 + cos t) , 0 < t < 27 .
A: we have been given the parametric curve x=(cos t)(1+cos t) and y=(sin t)(1+cos t) where 0≤t≤2π
Q: r(t) = (e-t cos t, e-t sin t, e-t)
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Q: 1. Find the tangent to the curve given by the parametric equations: X = 1/t; y= VE e-t
A: Appliaction of derivative problem
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- Find the parametric equation for the line tangent to the r(t)=sinti+(t2-cost)j+etk curve t=0 at the parameter value.Find the slope of the tangent line to the parametric curves x=3t+2, y= 2t^2+ 3t-3 at t=11 and then check your answer by eliminating the parameter.Find parametric equations for the semicircle x2 + y2 = a2, y> 0, using as parameter the slope t = dy/dx of the tangent to the curve at (x, y).
- Find parametric equations for the line that is tangent to the curve r(t) = e^t i + (sin t)j + ln (1 - t)k at t = 0.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?Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point ->(5,0,0). x=5e^t, y=te^4t,z=te^(t^5)