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Numerade Educator

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Problem 30 Easy Difficulty

Find three different surfaces that contain the curve
$ r(t) = t^2 i + \ln tj + (\frac{1}{t}) k $.

Answer

$y=\ln \sqrt{x} \quad z=\frac{1}{\sqrt{x}} \quad z=e^{-y}$

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Video Transcript

for this problem. We have a vector equation and we can write X equals t squared y equals the natural log of T and Z equals one virtue. So with that, we can write that y is equal to the natural log of T and we know that the natural log of T is just the natural log of the square root of t squared. That's just some way that we could write it, because now what we can do is say that that's the same thing as the square root of X. Then for Z, we can write that this is one over t but we know that that's the same thing as one over the square root of T squared which is just one over the square root of X. And then lastly, we can write Z as one over t which equals one over E to the y, which equals E to the negative one. So what we've seen is that by rewriting this, we can get things in terms of y and X. Uh, so this right here will be Our final equations are final solutions to the