Question

solve: lim->-∞ l3-xl + x

Answer 1

Do you use piecewise funtion?

Answer 2

Please explain step by step

Answer 3

try substituting x->-x because of which your limit becomes ∞ from -∞

Answer 4

i don't get it, why would i do this?

Answer 5

then you'll have
|3+x| -x with x->inf

this'll help you take care of the mod

Answer 6

i've already solved for +inf, answer is inf.

Answer 7

answer according to be should not be inf

Answer 8

I thought we'd already done this?
http://openstudy.com/study#/updates/51c6fb73e4b069eb00c5dc53

Answer 9

yes, but i'm still struggling

Answer 10

i'm just more confused now

Answer 11

Okay, so let's have a look at that function again...
\[\large f(x) =|3-x|+x\]

Answer 12

And see how it behaves. Int particular, the
|3 - x| bit.

Answer 13

alright; so what do i do to solve it?

Answer 14

are there different methods?

Answer 15

I'm sure, but I'm not familiar with them. Better check back with @shubhamsrg :D

Answer 16

i just had 1 method in mind, to substitute x for -x :|

Answer 17

still different :)
I expressed as...
\[\Large f(x) = |3-x|+x = \left\{\begin{matrix}3& \qquad x\le3\\2x-3&\qquad x>3\end{matrix}\right.\]

Answer 18

(Y)

Answer 19

shouldn't it just be: l3-xl = (3-x) if x >3
-(3-x) if x<3

Answer 20

Okay, here's the thing...
first things first,
|a| = a if a>0
|a| = -a if a<0

catch me so far?

Answer 21

yea

Answer 22

Okay... now if
x > 3
Then...
0 > 3-x
correct?

Answer 23

yes

Answer 24

Well then, flipping it around, we get
3 - x < 0

Answer 25

alright

Answer 26

Well then, 3 - x < 0
which means
|3 - x| = -(3-x) = x - 3

Answer 27

wow what

Answer 28

oh ok, i get it

Answer 29

We said that if a < 0
then
|a| = -a

Answer 30

3-x is no exception.
Since 3 - x < 0
then
|3 - x| = -(3 - x) = x - 3

Answer 31

yes, you put the minus to get a positive again because its an absolute value

Answer 32

Yup.
So you understand that
IF x > 3
then
|3 - x| = x - 3

right?

Answer 33

yes

Answer 34

Okay, from that same logic, what if x < 3?

Answer 35

i don't know

Answer 36

i thought -3-x

Answer 37

well, let's subtract x from both sides giving us
0 < 3 - x

Or
3 - x > 0

From this, what can we conclude?

Answer 38

i give up

Answer 39

a > 0
then
|a| = ?

Answer 40

And giving up is not allowed. Particularly during quizzes or exams :P

Answer 41

just a

Answer 42

Yup.
so
|3 - x| = ?

Answer 43

3-x?

Answer 44

Yes.
So, recap so far.
If x > 3 then
|3 - x| = x - 3

And if x < 3 then
|3 - x| = 3 - x

catch me so far?

Answer 45

they're both the same?

Answer 46

i should write this down, might make more sense

Answer 47

No, they're not. They're negatives of each other.

Answer 48

how come you say: -(3-x) = x-3

Answer 49

What else could it be?
\[\Large \color{red}-(3-x)=\color{red}-3 \color{red}--x = -3+x = x -3\]

Answer 50

haha, stupid question (tired)

Answer 51

but anyway, i get it

Answer 52

i wrote it down and it makes sense

Answer 53

Okay, that said...
If x > 3
implies
|3 - x| = x - 3
then what bodes for
|3 - x| + x = ?

(PS avoid maths when you're tired. It could lead to so many errors.)

Maybe you should rest? :D

Answer 54

haha, no i need to get this ;)

Answer 55

Well then, I had a question for you ^

Answer 56

2x - 3

Answer 57

How?

Answer 58

x - 3 + x

Answer 59

Very good.
I just wanted to make sure you understand :)
And what does
x < 3
imply for
|3 - x| + x
?

Answer 60

3 - x + x = 3

Answer 61

Good :)
So now, I take it you understand why
\[\Large f(x) = |3-x|+x= \left\{\begin{matrix}3& \qquad x\le3\\2x-3&\qquad x>3\end{matrix}\right.\]?

Answer 62

phew, yes

Answer 63

Well then, you'll notice that as x goes to negative infinity, ALL THOSE NUMBERS are going to be less than 3, so the value for f(x) will always be...?

Answer 64

3

Answer 65

And hence the limit :)

Answer 66

aaalright, thx!

Answer 67

No problem :)

Answer 68

thx for your patience too

Answer 69

Sure :)

Answer 70

and the question can be closed! woohoo

Answer 71

I'd just like to point out that when x = 3 (we didn't cover this)
then |3 - x| + x = 3 = 2x - 3

That is to say, when x = 3
it doesn't matter if you define f(x) to be 3 or 2x - 3
it'll be the same value.

Answer 72

i see

Answer 73

thx again

Answer 74

But that doesn't affect the nature of this question. It was just a thought.

Answer 75

yea

Answer 76

Close away :)

Answer 77

alright, till next time!