Question

lim x→+3 |x-3|/(x-3)

Answer 1

when x-> +3; assume that x is a little greater than 3
I can write it as x = 3+ y ; where y is some very small qty >0.
Now I will put the value of x in the given expression and find the answer.

Answer 2

\(\bf lim_{x \to 3} \cfrac{|x-3|}{x-3} \implies
\begin{cases}
lim_{x \to 3^-} \cfrac{-(x-3)}{x-3}\\\quad \\
\bf lim_{x \to 3^+} \cfrac{+(x-3)}{x-3}
\end{cases}
\)

Answer 3

|3+y-3| /( 3+y-3)
= |y|/y

Answer 4

Remember y >0

Answer 5

so its 0?

Answer 6

oh

Answer 7

oh No

Answer 8

is it 3?

Answer 9

Do you understand this symbol | |

Answer 10

yes

Answer 11

modulus sign

Answer 12

What does it do?

Answer 13

absolute value

Answer 14

hmmm, I understood as |x-3| not [x-3] or [[x-3]]

Answer 15

yeah if the number is greater than 0 it keeps the number as it is
for e.g |2| =2
when the number is less than 0, it inserts a minus sign to it
e.g |-2| = -(-2)

Answer 16

the limit is 1 for positive x and -1 for x negative

Answer 17

oh i see isee

Answer 18

the answer is 1 because its only asking for the right side

Answer 19

hmmm I saw +3.... not \(\bf 3^+\) maybe it's just me

Answer 20

x ->+3 means x is greater than 3
So I write x = 3 +y (y>0 and very small)

Answer 21

I meant it as x approaches 3 from the right side

Answer 22

c=3

Answer 23

limit dne from left side right?

Answer 24

limit is done from both sides

Answer 25

as jade said it is x-> +3
You need to find limits from both sides

Answer 26

from right as well as from left

Answer 27

When you approach from the left, let x = 3-y

Answer 28

its only asking for the right side though, isnt it? with the notation +3

Answer 29

No it is telling that x is approaching +3 and NOT -3

Answer 30

this section is about one sided limits

Answer 31

It can approach +3 from both sides left as well as right

Answer 32

+c and -c

Answer 33

yeah

Answer 34

so it approaches one from the left side as well

Answer 35

i mean -1