Question

Can someone explain this limit to me?

Answer 1

do you understand how the absolute values work?

Answer 2

yes

Answer 3

so
\[\lim_{x \rightarrow 1^{-}} \frac{ -2(x-1) }{ (x-1) }\]

Answer 4

then you can cancel out the (x-1)s so you're left with -2

Answer 5

How do you know when a limit is infinite or not?

Answer 6

um, when as you get ever closer to the limit value, the number increases... would you like me to find and show you an example?

Answer 7

an example to show when a limit is infinite
\[\lim_{x \rightarrow -3^{-}}\frac{ 1 }{ x ^{2}-9 } \rightarrow \lim_{x \rightarrow -3^{-}}\frac{ 1 }{ (x-3)(x+3) }\] can not be factored down any more so plug in a number that is less than but close to -3 so
\[\frac{ 1 }{ (-3.01-3)(-3.01+3) } = 601\] but as you get closer to -3
\[\frac{ 1 }{ (-3.001-3)(-3.001+3) } = 6001\] and the dramatic change in the size of the number is such so that the limit is +∞

Answer 8

How can you tell that its not infinity for the absolute value question?

Answer 9

because you are left with a solid answer.

Answer 10

Okay thank you!