What do you mean by points of continuity of a function?

Question

wat do you mean by continuity and discontinuity

Answer 1

I'm not sure what level you're at... but I'll go for a slightly simpler explanation. Imagine a graph of y=x. All points on this graph are continuous - they are all connected in an unbroken line.

Now take a look at y=1/x. This function has a point of discontinuity at x=0 - the graph suddenly jumps from a very negative number (ie at x= -0.001, y = -1000) to a very positive number (at x = 0.001, y = 1000)

There are many other graphs, which might have more or less complicated formulae that are discontinuous.

The definition of a point of continuity is that if you look at a point (x,y) on a graph move a tiny fraction to the left of x, and a tiny fraction to the right along the graph, then the answer, y, will be the same. Wrap that up in maths speak then you can apply it to multi dimensional graphs and complex functions that hurt your head.

Answer 2

continuity means the graph of the function has no breaks at that point .discontinuity means opposite to it .

Answer 3

Discontinuity means that there are restrictions on the range and domain so there are open circles on numbers that are not included and closed circles on numbers where the line of the graph starts. It may be a step graph too.

Answer 4

A "continuous function" means that there is no "break" in its graph. Since we all know that in every function, for every value of x there is exactly one corresponding value for y, then you may interpret a function as one that starts from the "left" and ends on the right". However, if you take any interval from that graph, and there is a "break", then that function is not continuous on that interval.

^_^

Answer 5

the standard definitions of differentiability: d/dx f(x) = lim(h->0) [ (f(x+h) - f(x)) / h ] or df/dx (a) = lim(x->a) [ (f(x) - f(a)) / (x-a) ] For the two a variety of, on each and every occasion a function is differentiable, it would desire to be non-end. although, we nonetheless could have purposes like the f(x) = |x| which has a corner at x=0, so it fairly is non-end, even though it fairly is not inevitably differentiable. many of the nitty-gritty: The "function with a hollow" isn't differentiable on the hollow, through fact we can't placed the "f(x)" or the "f(a)" into the definition. i think shall we make a various definition of the spinoff for incomplete areas, yet then there'd be no reason to not do the comparable for the continuity, subsequently making the hollow fairly non-end.

Answer 6

it is continuous at x if h->0 f(x+h) = f(x) when h >0 ->0 and h <0 and h->0

for example sin x

it is discontinuous if it is not so

for example take tan pi/2 h is >0 and ->0
pi/2-h is in 1st quadrant and tan is + inf
pi/2 + h is in 2nd quadrant and tan is - inf
so it is discontinuous at pi/2

Answer 7

POINT OF CONTINUITY SATISFIES FOLLOWING CONDITIONS, 1] f(p) is defined at that point ...{say p is point of continuity} 2] Right hand limit of x-> p & left hand lim. of x->p both exist 3] Both limits are equal 4] Limit is equal to f(p)
If these conditions are satisfied that point is point of continuity