Question

1. Give five examples of Uniform
continuous function and non-uniform
continuous functions​

Answer 1

Answer:

Continuity at a particular point  P  is like a game: someone challenges you to stay within a given target precision, you respond by finding a small region around  P  within which the function doesn't wiggle outside that precision. If you can win this game no matter how tight your opponent makes the precision, the function is continuous at that particular point  P .

If you want to check continuity at a different point  Q , the game starts all over again. Opponent challenges, you respond. Your responses in the game around  Q  may be totally different from your responses around  P . Different area, the function may behave differently there, it's a new game. If you win this game, too, the function is continuous at  Q  as well.

If you can win all such games around all points in some region  A , the function is continuous throughout  A . But the way you win those games can, again, be different for different points in  A .

Uniform continuity flips this around: we're now playing a single high-stakes game for the entire region  A , in one shot. Your opponent challenges you with a precision, you respond by finding some radius that has to work around any point  P  inside the region  A . That same radius must make the function not stray beyond the allowed precision anywhere.

Here's a simple example. Take a simple function like  y=3x , and look at its graph.

Step-by-step explanation:

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