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October 15, 2025, 06:17:52 am
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Author Topic: TyErd's questions  (Read 43325 times)  Share 

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brightsky

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Re: TyErd's questions
« Reply #405 on: July 03, 2010, 12:29:47 am »
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The fundamental theorem of calculus is basically just the basic ideas related to integration, differentiation, indefinite/definite integrals, etc. Don't think you need to know the real details of it and where it came from but it's useful to understand; the actual "statements" of the theorem you would've already known, like integration is the opposite of differentiation, etc.
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/0

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Re: TyErd's questions
« Reply #406 on: July 03, 2010, 02:55:23 pm »
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All you need to know about the fundamental theorem of calculus is this:

, where
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TyErd

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Re: TyErd's questions
« Reply #407 on: July 03, 2010, 03:16:55 pm »
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okays thnx /0 , how do you simplify this:
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brightsky

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Re: TyErd's questions
« Reply #408 on: July 03, 2010, 03:31:23 pm »
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Imagine it on a unit circle. For , we are given the angle , then rotate that around radians. We end up in the 3rd quadrant (but the angle is still the same by symmetry), which is negative for cosine, hence it becomes . Same deal for .
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TyErd

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Re: TyErd's questions
« Reply #409 on: July 03, 2010, 03:44:07 pm »
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Thankyou again brightsky, clear as always :)
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TyErd

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Re: TyErd's questions
« Reply #410 on: July 03, 2010, 06:00:40 pm »
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the.watchman

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Re: TyErd's questions
« Reply #411 on: July 03, 2010, 06:02:24 pm »
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TyErd

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Re: TyErd's questions
« Reply #412 on: July 03, 2010, 06:14:26 pm »
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thanks the.watchman

I have another problem:

the rate of flow of water from a reservoir is given by ,

where is measured in millions of litres and is the number of hours after the sluice gates are opened.

Find

a) The times when the rate of flow is maximum
b) The maximum flow
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brightsky

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Re: TyErd's questions
« Reply #413 on: July 03, 2010, 06:36:59 pm »
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The maxima or minima exists when the derivative = 0, so:





or

or

Substitute the values for t back into the original equation:

or

Hence clearly a) is t = 0 and b) is 1000.


I think is also an answer, because by letting the derivative = 0, we are only finding the turning points, but with a restricted domain, t = 15 also yields .
« Last Edit: July 03, 2010, 06:41:11 pm by brightsky »
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TyErd

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Re: TyErd's questions
« Reply #414 on: July 03, 2010, 06:42:53 pm »
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hm.. the back of the book says the answer for a are t=0 and t=15. I got the same answers as you as well.
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TyErd

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Re: TyErd's questions
« Reply #415 on: July 03, 2010, 06:43:19 pm »
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lol damn beaten
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TyErd

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Re: TyErd's questions
« Reply #416 on: July 03, 2010, 06:44:27 pm »
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Do you know how to get 15 with working out?
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brightsky

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Re: TyErd's questions
« Reply #417 on: July 03, 2010, 06:45:51 pm »
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Yeah, for the {x:dy/dx = 0} method, we're only finding the local maximum/minimum, but in your case, we need a global maximum, which is really just one step more. We know that the largest "y-value" in this case is 1000, so we substitute dV/dt = 1000 and solve for t to get the other t = 15 answer.
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TyErd

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Re: TyErd's questions
« Reply #418 on: July 03, 2010, 06:48:20 pm »
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OHH okayys thankyou heaps!
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TyErd

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Re: TyErd's questions
« Reply #419 on: July 03, 2010, 06:48:46 pm »
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oh yeah another problem What are the coordinates of the point of intersection of the graphs
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