Sunday, February 3, 2008

Limits

What is Limits

Why is limits needed in maths

What is the purpose of limits with respect to graphs

Why is limits used in the delta process

40 comments:

master_cookie said...

well this the master here again. to me, i understand limits to be like a restriction that shows or tell someone when they can stop. for example, if they were doing something, a "limit" is there to tell them that it can be done only up to that point the "limit" ,i.e. restriction, allows it to be done.in maths, for example the topic SETS,a question may ask u to find the set of positive numbers, but without "limits" to stop or "guide" you, you would be counting from now till eternity and not evening passing the number 2. well u don't believe me eh? well...let me explain. without limits u will have to include the fractions of numbers and fractions alone are infinite. so when we introduce "limits" into the equation, we can set boundaries to guide or shows as when to stop. for the sets example i talked about before, when we put limits into play we can introduce boundaries to tell us to only include the whole numbers between 1 and 20. i hope this explains limits . comments are accepted.

Fariel Mohan said...

master_cookie
I like you thought on limits
Very interesting
Hope to read some more like this

bird said...

limits? To me i understand a little. It means that you can only reach a certain point. Example a car has a certain speed "limit". It cannot exceed or else the car would malfunction. For example in maths, fractions have no limit. The 22/7 pi function can never be a decimal becase there is no limit. The number keeps dividing and hence we use an approximation.

bird said...

limits is used in the delta process to arrive close to a number without ever touching it on a graph. The line tends to the number but never touches

sweediekinks said...

Well said master_cookie!
Limits are espically important in trying to find the gradient of a curve for instance. Limits act as a guide, it lets you know if you on course or if you're off. It helps you to visualize on the graph where the value may tend to be. I'm not sure on this one but I think that limits is used in the delta process to give a guide as to what the value of the change in height(delta h) may tend to be for a gradient to be of a certain value. The value of (delta h)may tend to the number but because it is not exact in value they will not touch.

variable 47 said...

Limits are parameters or threashholds that keeps something within a particular region of operation. limits are needed in maths because some situations demand limits in order to produce a practical solution. e.g. 1/3 = 0.333333 recuring. The limit to this which would make this practical can be something like 1/3 to the first three decimal places. limits are needed in graphs in order to detail the parameters of mathematical operations eg. a graph for a function can be plotted for values of x to be between certain values such as the values of x from -5 to +5.

cruiser said...

thanks master cookie i would like to think of it as a guide to know when to complete something. I would like to think of it as a race At the beginning you would take of then in order to complete the race you must have a finish line. Without a finish line the athletes would never stop if there was no finish line or limit.

ichigo said...

If F is a function and A and B are numbers in which x is close to A but not equal to A then F(x) is close to B.
When x gets closer to A but not equal to A then F(x) is closer to B
limF(x)=B
x-a

lilo said...

a limit in any equation like what master cookie said is 'a restriction 'it sets up a standards or boundaries. For example take the equation y = 2x, the value of x could be any value, one cannot really know. Now using a limit for this expression:
y= 2x
lim x=2
This shows that the limit of x is 2 and so the value of x is known and the value of y can be found

Bootz said...

i never really understood limits at school so if i tried to answer what a limit is i would be lying, so if anyone can break it down for me as to what limits is with practical examples then i am sure i would understand it thank you.

Tazmania said...

i understand limits to be very practical in the real world, since everything that you are doing requires u to stop at a certain point. without limits you will be going on and on like cruiser said a race without a finish line. am not quite sure about the delta process, can someone enlighten me on that one, thanks.

yoshi said...

with respect to graphs consider the tan graph which approaches infinity as the angle reaches 90 and 270 degrees. Limits are needed to stop plotting at the points given.

marz said...

hey bootz wel let me try to explain the limits as master cookie said . that person had the simpliest eg. it is where u go to a certain line but u dont touch or cross that. because that is the limit. like on graphs it is used to find the gradient at every point on the curve

Brainiac said...

Well for me "limits" means a point or line or boundary that you cant cross or go further.For example,in biology the enzymes in the body functions up 2 a certain temperature it is "limit" to, if it crosses it will die.In relation to maths "limits" can defined as how far a number exceeds to its stopping point.Do you understand what i am saying?

cokebaby said...

the term limits is a very important term since it indicates the point at which sumting cannot exceed. for example if u are to plot a graph and u are given the range -3>x>3...this range refers to the limit in which the graph cannot exceed..i tink. correct me if im wrong. in graphs limits can also be used to find the area under a curve by integrating the function, substituting each limit into the integral and subtracting both.

boo boo boy said...

Limits are important for graphs escpecially curved graphs because the gradaint on a curve is changing at every point, therefore it is impossible to find the gradiant at any one specific. Here is where limits come in. Limits are like your close neighbours so if you want to get a particular for look for the neighbor / limit closest to that point.

cokebaby said...

y is limits used in the delta process? first u have to ask urself wat is the delta process? It involves gradiant. Rembember gradiant involves two points. consider these two points as A and B. The gradiant of AB = Change in Y / change in X. As B approaches A the change in x approaches zero. True?? therefore..umm.. i kinda stick. HELP!!

MOoSe said...

limits mmmmm limits has to deal with the extremities of something

MOoSe said...

limits is needed in maths because there needs to somepoint where an anwser to a problem is correct. if for example you want ot list the numbers that are > 3 since numbers never reach a limit we will be countin for eternity so if i set a limit i wil get a more reasonable answer

Dante' said...

I agree with master cookie because explained everything in detail. also limits can be used on a graph to state the stop or end point to the curve or straight line.

Dante' said...

whst does the delta process influence on the gradient? is not the delta h the value that is closest to the the gradient change? i confused...

xxxyyyz said...

limits is a general word where it can be said tat there is a limits to evrything....i.e.something which cannot be crossed out of boundary or a point.....in maths limits means tat the problem should end some wher or within a certain point....:):):)

rodriguez said...

the limit of a function is an important part in calculus. It concerns the behavior of a function near a particular input. in basic words, a function assigns an output f(x) to every input x. The function has a limit L at an input p (max. or min.)if f(x) is "close" to L whenever x is "close" to p. Limits are evident in our everday lifes; examples are found in travelling;Imagine a car driving over a landscape represented by the graph of y = f(x). Its horizontal position is measured by the value of x, Its displacement is given by the coordinate y. It's driving towards the horizontal position given by x = p. As it approaches, it notices that its displacement approaches L. If later asked to guess the displacement of x = p, it would then answer L, even if it had never actually reached that position.
limits can therefore be taught of as boundaries or border lines.

Bootz said...

thank you very much marz you didnt have to make me look that dumb its just that i understand that part but when you have to actually apply this to a problem thats where i get stuck but thatnks anyway.

Copy Cat said...

limits is at some level where u stop. that is limits in with respect to graph is where u stop or there is a boundary at that cordinate (eg) lim x tends to 3 and f(x)=2x, now u can say the when x tends to 3 the limit of f(x) is 6.if u need more clarification just ask.

Anonymous said...

limits is like a border at where you are supposed to stop.it can also be considered a restriction. eg a restricted area is an area where limited people has access to.

Dante' said...

i think it is known as a boundary or stopping value, whatever you may call it, to a certain activity. for example to discover the points on a graph, a limit to the x value can be given to calculate the coordinates of that point.

sweediekinks said...

kervin u on point there boy; that's some good stuff you're saying!

dark angel said...

i think that limit is define as its name which is only up to a certain boundary and is use in maths to find the gradient of a curve.

dark angel said...
This comment has been removed by the author.
Bootz said...

ok so limits is the end point of a problem or like what matercookie said it is simply a guideline to something like for example when you are cooking there a guidlines as to what to do and what not to do.

Bootz said...

i think limits is needed in maths because if you do not have an end point you will never be able to finish any given problem

Bootz said...

with respect to graphs if you do not have an end point then the graph will never end it will keep on going

apocalypse said...

The limit utilizes the definition of a derivative of a function. it is very important because some problems which i have attempted may not work or may take longer with the differentiation rules.

my_light said...

well let me say that i kinda missed that class so i really din't understand but after reading master_cookie i think i undersatnd but master_cookie why cant u get infinite or zero, zero is still a number y dont u want to get infinite or zero.explain

Anonymous said...

limits is the behavior of a function as it gets close to some point

kelz said...

i think limits is the maximum point that can be reached or the level or line beyond which something doesn't or may not exceed or pass..if there is a limit for something it means that it is like confined by boundaries and the limits being the greatest or smallest amount permissible. i think limits is used in the delta process to be most precise or to obtain the closest value possible without crossing the boundary or number...amm i think. and with respect to graphs there could be a range for the graph which can be thought of as the limits. in finding the gradient of points on a curve graph limits can be used if the gradient of a point has to be found the closest point to it within a limit can be used. i'm not quite sure though...still a bit confused.

Dante' said...

limits can also be defined as the boundary of which the the equation is to be met, eg. in the relation to pressure against volume, the ln function is to be used to find the answer, i think.

say wa said...

master_cookie has pointed it out very clearly about the limits, but the limits states the cut off where it reaches the max, we need limits in maths to show the boundaries of wat to go up to, the cut off ponit.
i could not of stated it better, if there are no limits people would have no stop, in everything there are stop , to keep a control over things


limits are used in delta process to show where the change in gradient occurs

Dante' said...

oh yeah, limits can also be the envelope of a boundary. its a metaphor.