Let C be the curve defined by the parametric equations x = t2 and y = t3 − 9t. Find d2y/dx2.

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A: Topic- application of derivatives and tangent equation

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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: Find the slope of the curve whose parametric equation is given by y = t³ + t²+ 1/t and x = t⁴ + 3t²…

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Q: find the slope of the parametric curve x=-6t-5, y=3t^3, at the point t=3

A: To find the slope we have to find dy/dx For that we find dx/dt and dy/dt first

Q: : Find the length of the following parametric curve. x = 6 + 1", y = 1 + 7t21/2, 0 st s 2.

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Q: Find of the parametric curve x = sect, y = tant, at t = dx? Select one: -3V3 -1 3V3 3y3 1 3v3 O none

A: Here we find the double derivatives value at t=π/3

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Q: The curve defined by any parametric equations X = f(t), y = g(t) is always a function.

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Q: consider the parametric curve x=t2 , y=9t-t3 . find dy/dx at t=2.

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Q: Consider the parametric equations: x = 2t2, y =t³. Find at the point t = dx? 8 without eliminating…

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Q: Consider the parametric curve C that is defined by C: x=t^3, y=t^2+t, −1≤t≤3. (b) Is the curve…

A: Consider the parametric curve C that is defined byC: x=t^3, y=t^2+t, −1≤t≤3. (b) Is the curve…

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Q: Find the length of the parametric curve: x = 2t + 1; y = t? – 3,0 <t < 5

A: Given that: x=2t+1,  y=t2-3,0≤t≤5To  calculate   dxdt  and   dydt,dxdt=ddt2t+1=2dydt=ddtt2-3=2t

Q: A curve C is defined by the parametric equations x(t) = 3 + t“ and y(t) = t° + 5t.Which of the…

A: Given,         A curve C is defined by the parametric equations xt=3+t2 and yt=t3+5t.

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Q: Consider the following parametric curve: x(t) = 3t^2 −6 and y(t) = 3t^4 −3t^2 +12t +10 Find the…

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Q: Find the dy/dx of the parametric equations given: x= 2t² – t and y= t³ – 2t – 1

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Q: Find for the parametric curve c(t) (t-1 – 5t, 41) at the point t = -2. dx (Use symbolic notation and…

A: Given problem:- Find dy/dt for the parametric curve c(t) = (t-1 - 5t, 4t3) at the point t = −2.

Q: Find the dx² for the plane curve with the parametric equations X = t³ – 4 and y = t2. -2 9t4 2

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Q: Find the equation of the tangent line to the curve defined by the parametric equations x(t) = t3 +…

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Q: Which is the graph of the derivative dyldx of the parametric equations x(t)= 3cos t and y(t)=3sin t…

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Q: Find the length of the curve C defined parametrically by C: r(t) = e' cos t, y(t) = e sin t, 0<t< T

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Q: Find the asymptotes of the curve defined by the parametric equationsx=φ(t)=1t−2,y=ψ(t)=tt−1.

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Q: Consider the parametric curve C: x=t³ + 1, y = t² – t,0 <t < 3. Find the equation of the tangent(s)…

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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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A: To find the equation of the tangent to the curve described by parametric equation x=t4+2y=t3+t3,-2

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Q: and y =- for tz 0. A curve C is defined by the parametric equations x= Vi +1 t + 1 dy (a) Find dx in…

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Q: Sketch the curve given by the parametric equations x= t³ - 1 and y= t² + t.

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Q: Consider the parametric curve given by the equations:  x(t) = t2 + 37t - 23 y(t) = t2 + 37t + 48…

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Q: Find ,Y, and of the given parametric equations dy d²y dx ' dx² d³y dx3 X = cost, y = 5 sin t in…

A: The given parametric equations,x=cost, y=5 sint