Question

if x approaching 3 from the left =22 and x approaching 3 from the right = 22 but the lim f(x) as x approaches 3 = 20. is the function continuous at x=3?

why or why not

Answer 1

?
if the limit from the left is 22 and the limit from the right is 22, then the "limit' cannot be 20

Answer 2

im given a piecewise

Answer 3

f(x)=
2x^2 +4 when x<3

20 when x=3

28-2x when x>3

Answer 4

and im asked to find the limit of
x to 3+
x to 3-
x to 3

Answer 5

piecwise or not, if
\[\lim_{x\rightarrow 3^-}f(x)=22=\lim_{x \rightarrow 3^+}f(x)\] then the limit is 22, not something else

Answer 6

the function is not continuous at the point x=3

Answer 7

ah the limit is 22, but the function is not continuous at 3 because it is not the same as the value of the limit there

Answer 8

why is that unklerhaukus

Answer 9

for the function to be continuous, it must have the same value as the limit

Answer 10

so since
\[\lim_{x\rightarrow 3} f(x)=22\] but
\[f(3)=20\] it is not continuous at 3

Answer 11

ok

Answer 12

Satellite73 has already said this but
The function is Only continuous at some point if the limit Exists And is Equal to the function at that point.

Answer 13

ok can you help me with this one
state the definition of a function f(x) which is continuous at x= a

Answer 14

Yes, actually this (following) statement is pretty confusing "the lim f(x) as x approaches 3 = 20."

Answer 15

i was wrong there

Answer 16

A function is continuous at x=a if \[ \large \space \lim \limits_{x\rightarrow a^-}f(x)=f(a)=\lim \limits_{x \rightarrow a^+}f(x) \]

Answer 17

(assuming the limit exists of course)

Answer 18

If \( \space \lim \limits_{x\rightarrow a^-}f(x)=\lim \limits_{x \rightarrow a^+}f(x) \) then the limit exists.