Find the equations of the tangents to the curve x = 9t2 + 9, y = 6t3 + 6 that pass through the point (18, 12).

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A: (a)v×w =i-j+k|v×w| =12+(-1)2+12=3|v×w| =3|v×w| =|v| |w| sinθ →(1)now,v.w =|v| |w| cosθ →(2)(1)(2)⇒…

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A: Use l hospital rule for finding the limit.

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A: ∫sec5x tanx dx=∫sec4x (secx tanx) dxusing formula∫fn(x) f'(x) dx=fn+1(x)n+1 +cHere , f(x)=sec4x ,…

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A: We will evaluate this double integral using polar coordinates.

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A: I am attaching image so that you understand each and every step.

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A: Given problem:- Find an equation of the plane with the given characteristics. The plane passes…

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A: answer is in next step

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A: Let's find.

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A: Solving

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A: cos(2u) =2cos2u -1

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A: We can solve this as follows:

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