Question

dont know anything about limit............ tell me please n help to study that chapter...........

Answer 1

hmmm, well start by thinking about some applications you could use just for the word limit (not in a mathematical sense) such as limit (highest possible thing) limitless (no limits) speed limit... etc. Limits can basically be applies the same way in math.

Now lets take a visual approach at the actual mathematical limit:

If, as "X" approaches "B" from both the left and right, f(x) will approach the single real number (L), then "L" is called the limit of a function f(x) as x approaches "B"

or:
\[\lim_{x \rightarrow b}=L\]

here is an example for \[\lim_{x \rightarrow 7}x+3\]

so let all your numbers slowly approach 7 (I'm only going to use around 3 for each, you'll still get the idea)

X f(x) X f(x)
6.5 9.5 7.5 10.5
6.9 9.9 7.1 10.1
6.999 9.999 7.0001 10.0001

notice we came from both sides of 7 because "X" must approach "B" (or 7 in this case) from both sides of the graph

as you can see, the numbers appear to be getting VERY close to 10 from both sides, there-fore you limit for this graph is 10!

for limits that do not exist (DNE)
if the limit for the positive side does not equal the limit from the negative side, the limit does not exist (DNE)

If you want me to continue just say.... cause this could get looooooong

Answer 2

thanx............ ya i want it....

Answer 3

kk, now i'll show you different types of limits:

infinite limits:

We say

\[\lim_{x \rightarrow 0}=\infty \]
if we can make f(x) arbitrarily large for all x sufficiently close to x=a, from both sides, without actually letting x=a.

We say

\[\lim_{x \rightarrow 0}=-\infty \]
if we can make f(x) arbitrarily large and negative for all x sufficiently close to x=a, from both sides, without actually letting x=a.

Limits at infinity:
ex:\[\lim_{x \rightarrow \infty}=0\]
\[\lim_{x \rightarrow -\infty}=0\]
These will produce limits that only exist at infinity

Answer 4

thanx............ is it all about the introduction part?

Answer 5

now i will show you some tips for actually solving these limits:

1. Direct substitution:
Direct substitution works well for any function that you know has no holes, asymptotes, or jumped in it (0/0 = hole, c/0 = asymptote)

ex: Lets look back at the very first equation i showed you for limits:\[\lim_{x \rightarrow 7}x+3\]
remember, after all that work we did, limit was at 10. We can use direct substitution to figure this out rather easily and painlessly
all we have to do for direct substitution is take the number "x" is approaching, and literally plug it in for x
(7+3=10)

and yes, that was the intro part :P

Answer 6

2. Sign analysis:
If direct substitution gives you a hole or asymptote (you get a constant/0) you can use sign analysis to solve it
ex:\[\lim_{x \rightarrow 4}2x \div x-4\]
notice if we do direct substitution, its give us 8/0, so we use sign analysis to solve it

2x - 0 + +
x-4 - - 0 +
0 4
+ 0 - infty +

notice how the graph will be from: \[\left( -\infty, \infty \right)\] Therefor the limit does not exist

Answer 7

3. Factoring:
Same conditions as sign analysis, only if you can factor it, DO IT!
ex: \[\lim_{x \rightarrow 2}x^{2}-4 \div x-2\] we can factor the top by using the difference of squares law

so \[\left( x+2 \right)\left( x-2 \right) \div x-2\] we can now cancel out the x-2's on the top and bottom \[x+2\] and now you can use direct substitution to achieve your answer \[2+2=4\] there-fore, your limit is at 4

Answer 8

wow.............

Answer 9

fml... i just had an adobe crash lmfao... and what wow? ;o

Answer 10

the answers what u had typed r really weird.... coz of ur adobe crash its written in such a manner that i cant understand....... its ok...... when u have it repaired then send me answers . okay?? thanx 4 alll.......

Answer 11

haha, kk, sorry about that :P

Answer 12

its okkkkkkkkkkk...@_@