Question

PLEASE PLEASE PLEASE HELP!!!!!!!! TT^TT

Find the indicated limit, if it exists.

Answer 1

@SolomonZelman @jdoe0001 @mathstudent55 @mathmate @Whitemonsterbunny17

Answer 2

@texaschic101 @aaronq

Answer 3

someone please help me

Answer 4

@SithsAndGiggles

Answer 5

The limit will exist if the one-sided limits exist as \(x\to0\) from the left and right.

What are the values of \(\displaystyle\lim_{x\to0^-}f(x)\) and \(\displaystyle\lim_{x\to0^+}f(x)\)?

Answer 6

For piecewise functions like this one, as \(x\to0^-\) (from the left), this means you would use the piece of the function that is defined for numbers to the left/less than 0, so
\[\large\lim_{x\to0^-}f(x)=\lim_{x\to0^-}(5x-9)\]
Similarly, for \(x\to0^+\), you have
\[\large\lim_{x\to0^+}f(x)=\lim_{x\to0^+}|2-x|\]

Answer 7

so how would I check for the limit?

Answer 8

(5(-1)-9)
2-1???

Answer 9

Well at this point you can substitute directly because the component functions \(5x-9\) and \(|2-x|\) are continuous.

And no, we're approaching 0, not 1.

Answer 10

ok

Answer 11

For example, the left-sided limit would be
\[\large\lim_{x\to0^-}f(x)=\lim_{x\to0^-}(5x-9)=5(0)-9=-9\]

Answer 12

and the right side would be 2?

Answer 13

@SithsAndGiggles

Answer 14

Correct. So the one-sided limits aren't the same, so the limit doesn't exist.

Answer 15

Thank you!! :)

Answer 16

yw