Question

Limits.

I've just started doing limits. i'm not very good at it..and i'm stuck with this question..plzzz help !!!

Answer 1

Where is the question?We will try to help you!!!

Answer 2

If f(x)= { |x|+1 , x<0
{ 0 , x=0
{ |x|-1 x>0
For what values of a does the \[ \lim_{x \rightarrow a} f(x) \] exists ?

Answer 3

\[\lim_{x \rightarrow a}f(x)=\lim_{x \rightarrow a+}f(x)=\lim_{x \rightarrow a-}f(x) =\] but where is the variable a in the equation.There must be in the equation to solve the problem!

Answer 4

the question's asking for the values of x which are represented by a sat "a" such that the limits exist at those values.

Answer 5

i think so...maybe

Answer 6

the Question meant we have to find all values of 'a' from -infinity to +infinity for which that limit exist.
now lets consider x< 0 , the function is defined as |x|+1 , for any valu os x, less than 0, the limit will be defined because we can always substitute that value of 'x' and get a real number as answer.
exactly same case for x > 0
so, that limit exist for all values of 'x' <0 and >0
now the only test point is x=0, we need to determine whether that limit exist for x=0 or not.
got this much ??

Answer 7

yes.:)

Answer 8

so, at x=0,
can you find these 3 limits,
\(\lim \limits_{x \rightarrow 0}f(x)=....? \\ \lim \limits_{x \rightarrow 0+}f(x)=...? \\ \lim \limits_{x \rightarrow 0-}f(x) =...?\)

Answer 9

whats the function ??

Answer 10

i mean i sit just 0??

Answer 11

f(x)= { |x|+1 , x<0
{ 0 , x=0
{ |x|-1 x>0

Answer 12

do you know what x->0
x->0-
x->0+ mean ??

Answer 13

f(x)={-x+1 B/c x<0
={0 x=0\
={x+1 B/c x>0

[\lim_{x \rightarrow 0}f(x)=\lim_{x \rightarrow 0+}=\lim_{x \rightarrow o-} then substitute 0 in each function

Answer 14

ya....i know that
i can solve the last two limits but how to solve the 1st one?

Answer 15

\(\lim \limits_{x \rightarrow 0}f(x)=f(0)=0\)
from
f(x)= { |x|+1 , x<0
{ 0 , x=0 <------------here
{ |x|-1 x>0

Answer 16

just substitute o on the function -x+1 forget about the minus sign

Answer 17

i got it .....

Answer 18

now that i look at this..it's not at all tough :p ..

thanks alot :D :D

Answer 19

thanks @neba.zi and @hartnn :)

Answer 20

yes, limits are simple and interesting :)
just to verify, what values of those 3 limits you got ? are they equal ? and whats your conclusion then ?

Answer 21

no they arent equal ..and the limit exist only for those values which are less than or greater than 0.

Answer 22

you are \(\huge \color{red}{\checkmark}\)

now welcome ^_^

Answer 23

:D thanks alot srsly..

Answer 24

my pleasure :) always happy to help :D