Define Electricity, Electronics, and magnetism?

Electricity:- Study of flow of current. Electronics:- Study of controlled flow current Magnetism;- Needed to study because we don't want any disturbance in above two phenomena.

Suppose that limx→c f(x) != 0 and limx→c g(x) = 0. Show that limx→c (f(x) /g(x)) does not exist.

Assume that limx→c (f(x) /g(x)) exists, and let L = limx→c (f(x) /g(x)). Then by the product rule for limits we obtain limx→c f(x)= limx→c {(f(x) /g(x)).g(x)} = limx→c (f(x) /g(x)) ⋅ limx→c g(x) where L = limx→c (f(x) /g(x)) Therefore limx→c f(x)= L ⋅ 0 = 0 . This contradicts the fact that limx→c f(x)!= 0. Therefore our assumption cannot be true: limx→c (f(x) /g(x)) does not exist.

Why are so many complex frequency related analysis developed to make our study more complex and difficult?

Analyzing frequency does a simple thing that it quickly tells us that there are so many signals at different time instant and so frequency analysis actually makes a bunch of signals have the same time period and directly facilitates us to know how many different signals we had during the whole time period. This advantage of frequency analysis generously proves its superiority over time analysis.