Question

Find all points of discontinuity of f, where f is defined by :

Answer 1

Someone's studying!

Answer 2

\[\large \binom{\begin{cases}
|x|+3& \text{ if } x\leq -3 \\
-2x & \text{ if } -3<x<3 \\
6x+2 & \text{ if } x\geq 3
\end{cases}}{}\]

Answer 3

Let's start with x=-3, okay?

Answer 4

Can you tell me what's the limit as x approaches \(x^-\)?

Answer 5

ok

Answer 6

isn't it \[3^-\]

Answer 7

Yeah, I meant \(3^-\), what's the lmit?

Answer 8

|x|+3 so -x+3 & x+3 right?

Answer 9

Note that \(|x|+3=-x+3\) for \(x\le -3\).

Answer 10

She's a girl?

Answer 11

:P

Answer 12

Anyways, what did you find for the limit?

Answer 13

I gave her a medal.

Answer 14

why is it just -x+3 ? what about x+3 ?

@Fool I know!!

Answer 15

Because x<=-3, right?

Answer 16

because of the constraints ..

Answer 17

diya you are not thinking :/

Answer 18

oh ok

Answer 19

That's not good thing ... Limit is a useful thing to understand ...

Answer 20

I will help you with this one. FOCUS!
\[\lim_{x\to -3^-}f(x)=\lim_{x\to-3^-}|x|+3=\lim_{x\to-3^-}-x+3-=-(-3)+3=6.\]

Answer 21

Can you find the limit as x approaches \(-3^+\)?

Answer 22

wait wait

Answer 23

\[\lim_{x\to -3^+}f(x)=\lim_{x\to -3^+}-2x=...\]

Answer 24

-2(-3)=6

Answer 25

Good! Are they the same?

Answer 26

I mean the left and right limit as x ->3?

Answer 27

lol Yes

Answer 28

What do you conclude then?

Answer 29

its continuos at -3

Answer 30

What about f(-3)?

Answer 31

f(-3)=-(-3)+3=6

Answer 32

Now, you can say that f(x) is continuous at x=-3.

Answer 33

Try to do the same with x=3, and write down what you get.

Answer 34

ok

Answer 35

diya just when right hand limit and let hand limits are equal, we can only say that that the limit exist at that point.

Answer 36

Find left limit, right limit and the value of the function at that point. If they are all the same then it's continuous at that point.

Answer 37

yeah i know that :)

Answer 38

Because you're smart! :P

Answer 39

Why does Diya have two medals and I only have one?! ::P

Answer 40

ok wait i'll do the rest

Answer 41

beacuse diya gives medals in the end!

Answer 42

lol

Answer 43

\[\lim_{x \rightarrow 3^+}f(x)=\lim_{x \rightarrow 3^+}(6x+2)=20\]
\[\lim_{x \rightarrow 3^-}f(x)=\lim_{x \rightarrow 3^-}-2x=-6\]
\[f(3)=6(3)+2=20\]
\[LHL \neq RHL\]
So its discontionous at 3

Right or wrong ?

Answer 44

Awesome!

Answer 45

You deserve a medal NOW!

Answer 46

Lol okay ofcourse You too!!

Answer 47

\[\huge THANK YOU \]

Answer 48

to both of you!

Answer 49

analyze how this incident will affect the over all
automobile industry?
diya can u please translate it in urdu >

Answer 50

nobody urdu here mam...

Answer 51

i dont know urdu sorry

Answer 52

oh:( jhooti