Consider the curve parameterized by a 3t2 15 and y= 2t3 15. Find equations for all tangent lines to this curve that pass through the point (-2,-3) Enter your answer as a list of equations, separated by commas.

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A: A detailed solution is given below

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A: Area between the y=sinx and x axis from x=0 to x=π

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A: Centroid is x¯,y¯ , where, x¯ = 1A∫ab xfx-gx dx  and y¯ = 1A∫ab 12 fx2-gx2 dxand A = ∫ab f(x)-g(x)…

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Q: Verify Green's Theorem by evaluating both integrals aN v? dx + x² dy | dA ду ax for the given path.…

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Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 3 1 lim tto0 2t2 +3' 2t (?,?)

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Q: Find the limit. NOTE: Enter the answer using round brackets. t2 +9 1 lim tto 9t2 + 10' 7t |(?,?)

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Q: what is the domain and range of f(x, y, z) = x + ln y + cos z (please explain)

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Q: Find the curvature and the radius of curvature at the stated point. r(t) = 8 cos(t)i +3 sin(t)j +…

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Q: Ex: Show that if v, u, w are any vectors, then (H.W.) ux (v x w) + v x (w x u) +w x (u x v) = 0.

A: Dot Product Property :- a.b = b.a = a*b*cosθ

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Q: 7) Determine the total area bounded between the function y = 1 – x between 1 and 1. -

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