Since this little program has generated so much discussion today (mostly via email), I thought I’d share how I used Jing tonight in a Virtual Office Hour…
This is right from my live chat tonight in my calculus class (my response to this problem is to follow up the 12 or so student posts)… the “cut and paste” part is because URLs are not “live” in the chat room. Plus I don’t want them to get accidentally booted out of “chat.”
me: The problem is to find the values of a and b in order to make the piecewise function continuous. Here’s the function (cut and paste URL into separate browser window) http://screencast.com/t/bbjcb3nrf
me: The only piece that you know for sure is the first one. Where is the problem value for the first piece?
student: at x=2 The first part is equal to x+2
me: so when x=2, what is y?
me: So now, in the second function we know it has to go through the point (2,4) or it won’t be continuous.
me: So, using y=ax^2-bx+5, substitute x=2 and y=4. You should end up with an equation that still has a and b.
me: Okay… now… the last two equations must also intersect at x=3. So we set these equal to each other and use x=3 because that’s where the last two pieces switch. http://screencast.com/t/ezrIzNJeDJ
student: why is it that we use x=3?
me: because that is where the function jumps from one piece to another and the functions must be equal at their endpoints to be continuous.
me: Now we solve the system of equations…
And that… is how you use Jing in a math chat! Each video took about 1 minute to upload… (but I’m on satellite high-speed internet, so probably it would be faster for most people with regular high-speed internet)
Please post your comments in the “comments” area (instead of in email) so that all readers can get the benefit.
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