/u/ptonsimp's posts in /r/calculus

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How do I tell the direction of the v(t) and a(t) vectors?? I assumed that a(t) must be perpendicular to v(t) because it’s the derivative of v(t) but that’s obviously not the case :/

24 upvotes

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The equation for this hyperbolic paraboloid is y=z^2 - (x^2/9). But how do I know which way it opens??

14 upvotes

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After multiplying part b’s power series function by x^2 to get part c’s, why do I need to replace the original n’s with n-2? Similarly in other problems, after I differentiate the original equation, I have to replace the n’s with n+1. I don’t understand why?

6 upvotes

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Through the Ratio Test, I got 0<1 meaning that the function is absolutely convergent. That makes sense. But at the same time, doesn’t the function fail the Alternating Series Test (where its limit doesn’t exist)? So would it not be conditionally convergent?

4 upvotes

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Title	Upvotes	Mark as read	Favorited	Rating	Add to a list
How do I tell the direction of the v(t) and a(t) vectors?? I assumed that a(t) must be perpendicular to v(t) because it’s the derivative of v(t) but that’s obviously not the case :/	24
The equation for this hyperbolic paraboloid is y=z^2 - (x^2/9). But how do I know which way it opens??	14
After multiplying part b’s power series function by x^2 to get part c’s, why do I need to replace the original n’s with n-2? Similarly in other problems, after I differentiate the original equation, I have to replace the n’s with n+1. I don’t understand why?	6
Through the Ratio Test, I got 0<1 meaning that the function is absolutely convergent. That makes sense. But at the same time, doesn’t the function fail the Alternating Series Test (where its limit doesn’t exist)? So would it not be conditionally convergent?	4