gradient = change in y
change in x
why then do I see gradient = lim change in y
∆h→0 change in x
What is the purpose of lim
∆h→0
Why is (x1, y1) always (x, y)
Why for (x2, y2) , x2 is always x + ∆h
What then is y2
In class we refer to a policeman, what is this policeman all about?
What is the denominator always and why?
What is the numerator always and why?
Why the numerator has to factorise to take out ∆h?
How can someone say where ∆h is substitute 0?
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45 comments:
the police man is simply being careful with ur positive and negative signs..for instance some one mite say - and - is a - or + and a - is a +.....u must be careful with the signs...
Can someone illustrate in your own words using an example maybe what policeman has to do with maths
It is very easy to make mistakes when doing problems so this is where policeman comes,example working a problem like this -2(3)+(-4)(-5)=? you have to be careful when multiplying and adding of positive and negative signs.
1. ∆h→0 indicates the change in height as the gradient tends to zero. Zero is your limit and is used in final substitution.
2. (x1,y1)are the first plotted coordinates on the axes and hence will always be (x,y).
3. x2 is the sum of the value of x1+ the change in height (value)between the points x1 and x2.y2 therefore will be the value of x2:(x+∆h)to the power of 2.
4. The "policeman" is the caution factor when expanding the equation. You have to pay attention to the sign(+/-) in front of the number to write its correct value. If someone does not do that the entire equation and answer is wrong.
5. The denominator must always be ∆h.The equation should contain common terms.
6.The numerator always has the term ∆h included in its value. It is important in factorising so that it can cancel out with the denominator.
7. The numerator has to factorise to take out ∆h as the like term so that it can cancel out with the denominator. This ensures that the answer after substitution is not 0/0,we don't want that.
8. When all the like terms are cancelled out and there is no denominator it is safe to substitute ∆h as 0 and get a logical answer.
1.delta h tends to 0; indicates that the limit for change in height must be equal to zero.
2.x1,y1 are your first chosen points used in the process of determinig your gradient(change in y/change in x)
3. x2 is the change between the first chosen x value(x1) and the horizontal distance between it. In some cases x2 is complicated to determine; therefore x+deltah is often used.
4.the policeman as explained in class acts as a caution factor when using the delta process. that is pay attention to proper use of signs and correct expansion of equations.
5&6.the equation must contain common terms in order for proper cancelling of terms; hence the denominator and numerator must contain deklta h.
7.proper factorising ensures that the terms do not cancel each other; thus making the answer wrong.
y=x+ change in x? delta H cannot equal to zero.The change in x how is this realated to a real life situation.
The policeman concept to my understanding is a strategy used when solving a mathematical problem. under exam conditions it is very easy to make errors with directed numbers, the policeman concept simply describes paying closer attention to negative number operations and after completing the computation involving the negative number return to your normal state of mind (so to speak).
how can we relate delta process to real life.
the denominator in the delta process in always delta h because you would always need that to cancel with the delta h in the numerator.
WHY IS THE DELTA PROCESS NECESSARY WHEN YOU CAN USE THE SHORT WAY BY USING THE FORMULA
the policeman is just a avenue that the teacher uses to remind you not to make mistakes. for example if you are doing the delta process and you removing brackets or something of that sort, when you see a minus and you have to multiply it by a bracket you slow down just like you would do when you are driving on the nations road
boo boo boy. we dont need the delta process but we were taught the delta process for us to understand where the formula came from.
(x1, y1) is always (x,y)because it is the first point plotted
x2 is always x+∆h because it is a small change in x , that is, the the values is very close to the x2 and ∆h is the small change like 0.0001 or 0.01
I think the policemean is a symbol whic we can use to be careful when doing these question.
Delta H .Whenever I hear or read about this I understand that this means a change in x or y .
firstly i do not understand the delta process so can ANYONE please help me to understand it thank you!!!!!!!!!!!!!
The policeman concept used in class is a method used so that you take your time and go slowly through the process and dont make any mistakes.It helps you to look closely at all sign so that you dont make silly mistakes.The policeman is there to show yiou that speeding gets you nowhere fast.Dont be in a hurry, you might make simple errors.
We say substitute zero because it represents the very smallest change that can occur.
policeman simply means to be careful wen multiplying positive and negative signs. for example....-(2x + 2)= -2x - 2
uupolice man in maths is the same as in real life. When u see a police, drive real slowwwwww. or take your time. When u see a (-) sign in maths..... just solve real slow or take your time
as i LEARNT IN CLASS.. the denominator is always ∆h. the reason for this is.. remember the first ting you have to do in the delta process is to set up ur X1,X2coordinates and ur Y1, Y2coordinates. Please note that ur X1and X2 coordinates are constants. You will always have to put X1 as x and X2 as x + ∆h ok.When these values are substitutes into the equation for finding the gradiant of a line the denominator would be X2 - X1 which is x + ∆h - x which would give ∆h. Its dat simple. with respect to the numerator (Y2 -Y1, Y1 will always be watever the equation is, and Y2 will be (x + ∆h) substituted into the equation. Understand?? When u have calculated Y2 - Y1. It is important that u take out ∆h to cancel with the denominator. ∆h represents a small change in x. This value of x is ever approaching 0. The distance between the 2 points gets smaller and smaller. Im not so sure about that part. someone care to help me??
∆h→0 is the change in height as the gradient(m) tends to zero and hence zero is your limit and is used at the last step as substitution.The police man simply means watch out or be verry alert of your signs.the denominator is always delta h because you have to cancel with the delta h in the numerator after simplifing.
policeman?????????? maths????????? since when you does get lock up for finding gradient of a line or working out logs miss or anyone please explain to me
I'm confused...where you all getting this policeman thing from?? first time I hearing dis!!!
moose and fredburger!!!! jus read my comment...its simple..Wen u all driving and u c a policeman, wat wud u do. Of course u would do the right ting by buckling up and driving cautiously.. True??? policeman simply means to be careful wen multiplying positive and negative signs. for example....-(2x + 2)= -2x - 2.. Wait! Wait! Wait! how come all yuh neva hear bout dis policeman ting. mummy mention dat soooo much in class. All yuh was in class??? Or all yuh was in d computer lab playn warcraft???
cokebaby how you droping it so hard on people? sometimes it does be hard to concentrate in class or sometimes you does get distracted and just didnt hear. maybe instead of using policeman mummy should use someting else.
maybe she should use something like when you see a negative sign its like a wet floor, if you move too fast you can slip.
the purpose of lim ∆h→0 simply means that the distance between the two points is decreasing. Its tending to zero. I tink!!! A little help here!!!!
ohhhhhhhhhhhh thanks mr. cokebaby inow undrestand the concept and please i was sick that day
cokebaby I made that comment too, and I'm still waiting for an answer to know if I am making sense. Maybe you can demand one judging by your previous tone!
miss the reason i didnt post any comments on this topic is because i dont understand it and i have asked around so as to be able to post a comment but the different explanations i got made me more confused.
wat popo....i doh kno wat is dis def. wit a policeman....
oh ok policeman means to slow down and take your time....ok kool...thanks cokes!...lol
to bootz:
you said you do not understand, i do not really kno y we do the delta process but if you follow these steps lik i do you'll finish the ques:
1)m=lim (y2-y1/x2-x1)
delta-0
2)(x,y)
(x2,y2)[x2=x+delta H]
3)(x,Y)
[x2=x+delta H]rewrite eq'n and where ever you see x put () and sub x + delta H in the ()
4) sub grad in the eq'n
and
5)simplify and then solve
that shud make it easier for you....ent?
thank you so much blessed08 i really appreciate your help hope that your explanation helps me
in the future
deta h has to be factored out in the numerator because you would need only one deta h term in the numerator.
Guys the issue of delta h tends to zeroimplies that like with neighbours there is always someone a closer distance to you . So the closer the distance the smaller the distance with respect to having a value.like there is 0.1 and 0.01,0.01is closer to zero than 0.1 and if you look closer there is 0.001 which is even closer to zero than 0.01 or 0.1.That is why we say delta h represents the smallest change and the smallest change is closest to zero than any other number.
yes ratman i remember that when miss was in my class she told us about the policeman she gave us a question like this one y=2xto be squared when the gradient limit delta h is 0 y2-y1/x2-x1,(x,y)is(x,2xsquared)(x2,y2)is(x + delta h,2(x+delta)to be squared then you just use the formula above, but when crossing outthe matching variable look out for the minus sigh where then the variable will equal to 0
sweediekinks has a good point, ∆h is the change in x where zero is the where x changes, i can't remember bout the policeman thing, according to boo boo boy is one who reminds us of any mistakes
the denominator is always x2- x1, because it is a measure the change in x at a point on a straight line, and the numerator is always be y2-y1 where it is the change in y on a staight line, the numerator has to factorise because ∆h= 0, and 0 over a number is undefine, and that's not a answer so we need to factorise it to remove the factor of being undefine
wat do all wan me 2 say u all more or less hav the same level of comprehending limits all i can but in is that for limits yur basically substituting values into the equation u form. so b careful of your signs when multiplying.
sweediekinks, kervin and cokebaby after reading your comments along with the rest there isn't anything really for me to say and i understood cokebaby's 2nd comment very well, i would like 2 thank all of you for clearing up everying for me and remember to look out for d policeman he checking alluh signs!!!
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