Jim, whle I appreciate that you've tried to help, none of your solutions are working. The problem is not with our computers. The problem is with Apple's update. THEY should be taking responsibility for this.
A call to Apple Care netted nothing. We turned off the laptop, reset it a number of ways, created a test user..., nothing. Except they noted I have an older laptop. This is way too coincidental to be a hardware issue and there's no good reason to have changed any drivers for a camera that was working.
Ironically, the update said it was supposed to add audio calling to FaceTime, except that doesn't work because the app can't find my camera. You just can't fix stupidity.
My only option is to Time Machine back to the day before I installed Mavericks which will also restore swiping within the few apps that some Apple bonehead removed it from. Of course, this then removes any updates to a variety of Apple and third-party applications as well as any new programs I've purchased that only work with Mavericks.
I'm not finding the forums to be very helpful these days, not because folks like yourself aren't trying but because Apple keeps doing things that just don't make sense.