1. For the parametric equations: x = 4t3, y= 2 +60t – 8t?, find: a) All values of t at which the tangent line has slope 1. d²y b) dx x2

Q: Use the parametric equations x= sec(t) , y=tan(t), for -pi/2 < t < pi/2. Sketch the curve…

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Q: Q/ Find the parametric equation for the line through the point (0, 1, 2) that is perpendicular to…

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Q: Determine which of the following parametric equations match the graph.…

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Q: 1.) Given the parametric equations: x=t'- 1 and y=f+t, find the 1ª and 2nd derivatives.

A: We will find the derivatives.

Q: Use the parametric equations shown below to answer the following. x = tV3 y = 3t - and

A: Given the parametric equations: (a) To plot the graph of these parametric equations using a…

Q: Consider the following parametric equations:   x= √t y=√(t−1) (a)  Sketch the curve represented…

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Q: Write the parametric equations as a function of x in Cartesian form. = x = 2t - 1, y = 6 - 3t

A: Given equation are x=2t-1 and y=6-3t

Q: 3t 1+f3.y te Consider the parametric equations x = 3t² ‡ 1+ 3,¹ -1. Its graph looks like this: = (a)…

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Q: Find a parmetric equation that describes the entire set of points (x,y) such that 4x2-9y2=36

A: The given curve can be represented in a different manner as shown on the whiteboard.

Q: Find the equation for the line tangent to the parametric curve: at the points where t = 5 and t =…

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Q: Consider the parametric equations x =t - sint and y = 1- cost. Which of the following dy ?…

A: If the parametric equations are  given byx=t-sin t  and  y=1-cos tThen to find the value of dydx.

Q: X=t +t ly=2t+3 t20 2.

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Q: Consider the parametric equations x t-Ssint and y = 1-cost. Which of the following represents dx…

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Q: consider the following set of parametric equations: x = 6tanhθ ; y = 3sechθ Calculate d^2y/dx^2

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Q: 10b. Find the parametric equations of the tangent line to the curve at t =1.

A: Given: The position vector is of a particle in space at a time t : r→(t)=&lt;t+1,t,1t&gt;=&lt;x, y,…

Q: 2a) Find the slope of the curve represented by the parametric equations, at 0 = T/6 %3D x = 5+ 3 sec…

A: The curve given is  x=5+3sec θy=-3+4tan θ

Q: Consider the curve described by the parametric equations ¤ = t² +4 and y = 3t + 4t. Determine the…

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Q: For the parametric curve x = t^2 + 2t + 1, y = 6t + 1, find the Cartesian equation(s) for all…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: Consider the parametric equations x = √t − 2 and y = (1/ 2)t + 1, t ≥ 2. What is implied about the…

A: Consider the given parametric equation as x=t-2 and y=12t+1