...What can you say about the continuity of this function?

Question

An electrical circuit switches instantaneously from a 6 volt battery to a 12 volt battery 7 seconds after being turned on.

Graph the battery voltage against time.

Give formulas for the function represented by your graph.

Answer 1

Okay, I'm not sure how giving a "real world" example that isn't physically possible will help your intuition, but since the battery voltage is stipulated to switch _instantaneously_ from 6 to 12 volts, the battery voltage is a piecewise constant function, which is 6 prior to 7 seconds and 12 after 7 seconds, with a jump discontinuity at 7. So you might have V(t)={6 if t<7, 12 if t>7}. Note that I haven't specified what the voltage is AT 7 seconds, because the problem didn't say either - I suppose you might make v(7)=9, and justify that by being the average of [t→7⁺]lim V(t) and [t→7⁻]lim V(t), but it doesn't make any physical difference, AFAIK.

Answer 2

x^2+x-2 =0 (x + 2)(x -a million) = 0 f(x) = (x-a million)/ (x-a million)(x+2) lim {whilst x ->a million} ( f(x)) = = lim {whilst x ->a million} (x-a million)/ (x-a million)(x+2) = = lim {whilst x ->a million} a million/ (x+2) = a million/3 function isn't non-end if x + 2 =0 answer: function isn't non-end at x = -2

Answer 3

You are in wrong section try electronics.