Question

to the limit?


(f ) lim f (x) for f (x) =
x→10
( log10 x if x > 10
x − 10 if x ≤ 10

(f ) lim
x→10−
f (x) = lim
x→10−
(x − 10) = 0 and lim
x→10+
f (x) = lim
x→10+
log10 x = 1.



Thus lim f (x) does not exist.
x→10

Answer 1

can someone esplain why this doesn't exist?

Answer 2

because the left limit and right limit do not converge to the same point.
you could think of it as a contradiction, therefore we say it doesn't exist

Answer 3

\[\lim_{x \rightarrow 10} f(x)=\log_{10} (x) if x >10\]
and \[f(x)=x-10 if x \le10\]

Answer 4

oh so its just the rule, that if they dont limit at the same point then its not possibly a limit?

Answer 5

yes because the way a limit is defined, there cannot be more than one limit for any given x-value, if so we say it does not exist

Answer 6

you're pretty smart for a dumbcow dumbcow.

Answer 7

haha thanks

Answer 8

you can't explain that further though can you?