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 October 6th, 2013, 01:45 AM #1 Newbie   Joined: Aug 2013 Posts: 24 Thanks: 0 Finding an expression for Instantaneous rate of change The question is - v(t)=250(1600-80t+t^2) Find an expression for the instantaneous rate at which water is leaving a pool at any given time, t minutes. This is my working - V'(t)=lim(h-0) 400,000-20,000t+t^2/h V'(t)=lim(h-0)400000-20000t+h+(t+h)^2-(400000-20000t+t^2)/h V'(t)=lim(h-0)400000-20000t+h+t^2+h^2+2th-400000+20000-t^2/h V'(t)=lim(h-0)h^2+2th/h V'(t)=h+2t V'(t)=2t Is this correct? Thanks October 6th, 2013, 02:08 AM #2 Senior Member   Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 522 Math Focus: Calculus/ODEs Re: Finding an expression for Instantaneous rate of change Now that's not correct. I would work the problem, assuming we are to use first principles, as follows: Now, let's rewrite the volume function a bit: Let's next make the substitution: and so we have: And so, we may write: Now, back-substitute for October 6th, 2013, 02:14 AM #3 Newbie   Joined: Aug 2013 Posts: 24 Thanks: 0 Re: Finding an expression for Instantaneous rate of change Thanks, I see where I went wrong, I didn't factorise the equation. Using differentiation, how would I do this? October 6th, 2013, 02:21 AM #4 Senior Member   Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 522 Math Focus: Calculus/ODEs Re: Finding an expression for Instantaneous rate of change If you use the rules of differentiation, you could write: Tags change, expression, finding, instantaneous, rate Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post swm06 Calculus 1 May 7th, 2013 06:14 PM tsl182forever8 Calculus 1 March 2nd, 2012 04:19 PM Pumpkin99 Calculus 1 September 26th, 2011 06:06 PM wicked357 Calculus 2 January 25th, 2010 10:21 AM mathman2 Calculus 13 October 20th, 2009 12:06 PM

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