Thanks jee..
waisay yeh Calculus mera most favorite subject hai.
On Thu, Nov 17, 2011 at 9:17 PM, bc110200816 Tasaddaq Hussain <bc110200816@vu.edu.pk> wrote:
you r Genius..........
On 11/17/11, Muhammad Umair <muhammad.umair.491@gmail.com> wrote:
> You're welcome jee...
>
> mujjhay bahut khushi hooi k aap ko samajh aa gaya..
>
>
>
> On Thu, Nov 17, 2011 at 8:48 PM, bc110200816 Tasaddaq Hussain <
> bc110200816@vu.edu.pk> wrote:
>
>> oooo bahot bahot shukrya Umair bhai sab theek theek se samaj aa gya
>> hay ap ne bahot achay tareeqay se explain kia hay ....Lectures se ye
>> mujay samaj nahi aa sakti thi .....
>> thanks a lot....
>>
>>
>> Allah ap ko Laaaaaaaaaaaaaaaaaaaaaaaaaaaaabi Umer de...
>>
>> On 11/17/11, Muhammad Umair <muhammad.umair.491@gmail.com> wrote:
>> > Limits ka matlab hai k agar hamara independent variable (jo k most cases
>> > mein x hota hai) agar kisi value ko approach karay tou us approach
>> karnay k
>> > nateejay mein function y=f(x) bhi kia kisi khas value ko approach karta
>> hai
>> > ya nahin....
>> >
>> > consider an example
>> >
>> > lim x->0 (1/x)
>> >
>> > x approach kar raha hai 0 ko... yaad rakhain k yeh limit hai, x kabhi
>> bhi 0
>> > k equal nahin ho ga... OK...
>> >
>> > 0 k qareeb kon kon si values hain....
>> >
>> > 0.01, 0.01, 0.001, 0.001, 0.0001, etc. etc.
>> >
>> > hmmm.. we are missing something.... ham postive side se tou zero le hi
>> > rahay hain .. par negative side bhi dekhtay hain
>> >
>> > -0.1, -0.01, -0.001, etc. etc. bhi zero k qareeb tar values hain...
>> >
>> > ab main nay x ko zero approach karwa kar 1/x ki values calculate ki
>> hain..
>> > see the following table..
>> >
>> > [image: math.gif]
>> >
>> > aap ooper table ko dekho, jab bhi ham 0 k qareeb se qareeb tareen jatay
>> > hain, tou 1/x kisi specifc value ko approach nahin kar raha.. balkeh
>> > hamesha increase hi hota rehta hai (magnitute mein)... jab aisi soorat e
>> > haal ho tou ham kehtay hain k limit exist nahin karti...
>> >
>> > i.e. lim x->0 (1/x ) exist nahin karti...
>> >
>> > agar ham aik aur example lain
>> >
>> > lim x->3 (x^2-9)/(x-3)
>> >
>> > tou function 3 par tou undefined hai, par limit exist karti hai....
>> kaisay?
>> > see the following table...
>> >
>> > [image: math.gif]
>> >
>> > ab aap dekho, jaisay hi ham 3 k qareeb se qareeb tar jatay hain, tou ham
>> > dekhtay hain k function 6 ko approach kar raha hai.. tou is case mein
>> limit
>> > exist karti hain aur 6 us ka answer hai..
>> >
>> > ab aatay hain graph ki taraf...
>> >
>> > *a- Limx---->1 g(X)*
>> >
>> > yaad rakhain k limit exist karnay k liay donon sides se limit ka same
>> hona
>> > zaroor hai.. OK...
>> >
>> > agar aap graph par nazar dorayain, tou nazar aaye ga k jab jab left side
>> se
>> > x k qareeb ham function ki value dekhtay hain tou pata chalta hai k y ki
>> > value 1 hai...
>> >
>> > jab k right side se agar ham dekhain tou nazar aaye ga k x ko right side
>> se
>> > 1 k qareeb dekhnay par y ki value 0 nazar aa rahi hai... aik baat aur
>> yaad
>> > rakhain yeh jo aik *bubble *sa banaya hooa hai graph mein x=1 par.. yeh
>> > discontinuity ko show karta hai, i..e graph x=1 par defined nahin
>> > hai....
>> > ok....
>> >
>> > limits donon sides se same nahin hain, is liay limit exist nahin karti..
>> >
>> >
>> >
>> > *b- Limx----->2 g(x)*
>> >
>> > donon sides se graph y=1 ko approach kar raha hai, tou is case mein
>> > limit
>> > exist karti hai aur us ki value *1 *hai...
>> >
>> >
>> >
>> > *c- Limx----->3 g(x)*
>> >
>> > donon sides se graph y=0 ko approach kar raha hai, tou is case mein
>> > limit
>> > exist karti hai aur us ki value *0 *hai...
>> >
>> > agar koi baat samajh nah aayi ho tou dil khol kar poochh lena
>> >
>> >
>> > On Thu, Nov 17, 2011 at 8:04 PM, bc110200816 Tasaddaq Hussain <
>> > bc110200816@vu.edu.pk> wrote:
>> >
>> >> In MTH101,
>> >>
>> >>
>> >> I have listen lectures about Limits more than one time but i could not
>> >> understand the Idea of Limit....Even when i started to solve some basic
>> >> questions, i find out the difficulties.....for example in the question
>> >> below i
>> >> could not understand that why limit is not exist at x--->1 and why its
>> >> 2, and 0 at next aproach...
>> >> I mean, my concept of the Limits is not clear so plz...........koi
>> >> mujy samjha de..
>> >>
>> >> For the function g(x) graph here, Find the following limits or explain
>> >> why they do not exist.
>> >>
>> >> a- Limx---->1 g(X)
>> >> b- Limx----->2 g(x)
>> >> c- Limx----->3 g(x)
>> >>
>> >>
>> >>
>> >> --
>> >>
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>> >>
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