Question

find the limit of lim x->3 (x-3)/(absx-3)

Answer 1

\[\lim_{x \rightarrow 3}\frac{x-3}{|x|-3}\] ?

Answer 2

left hand limit = lim x->3 (x-3)/-(x-3)=-1
right hand limit=lim x->3 (x-3)/(x-3)=+1
as LHL != RHL
i think limit will not exist .

Answer 3

absolute value of (x-3)

Answer 4

\[x>0 =>|x|=x\]
\[\lim_{x \rightarrow 3}\frac{x-3}{|x|-3}=\lim_{x \rightarrow 3}\frac{x-3}{x-3}=1\]

Answer 5

ok prashant did it for abs(x-3)

Answer 6

right hand side limit and left side limit are equal
when you approaching from left side as 2.999
it'll not be -x so in both case ans will be 1

Answer 7

no prashant is right the limit does not exist

Answer 8

if x=2.99 2.99-3/2.99-3=1
if x=3.011 3.011-3/3.011-3=1
what are you talking myiniaya it happens if x was appraoching zero

Answer 9

x is approaching 3

Answer 10

so as 2.99 it's not less than zero
mode (x)=x ,x>0

Answer 11

\[\lim_{x \rightarrow 3^-}\frac{x-3}{|x-3|}=\lim_{x \rightarrow 3} \frac{x-3}{-(x-3)}=-1 \neq 1=\lim_{x \rightarrow 3} \frac{x-3}{x-3}=\lim_{x \rightarrow 3^+}\frac{x-3}{|x-3|}\]
since left limit doesn't equal right limit
the limit does not exist

Answer 12

but you are doing another problem right?
you said if we are approaching 0?

Answer 13

it is mode (x) -3

Answer 14

not he said abs(x-3)