Question

Find the indicated limit, if it exists.

limit of f of x as x approaches 1 where f of x equals 1 minus x when x is less than 1, 8 when x equals 1, and x plus 7 when x is greater than 1

Answer 1

@amistre64

Answer 2

@satellite73

Answer 3

\[f(x)=\begin{cases}1-x&\text{for }x<1\\
8&\text{for }x=1\\
x+7&\text{for }x\ge1\end{cases}\]
For the limit to exist at \(x=1\), you need to have
\[\large\lim_{x\to1^-}f(x)=\lim_{x\to1^+}f(x)\]

Answer 4

\(\color{red}>\), not \(\ge\)

Answer 5

okay, this is all like a foreign language to me can you walk me through it...??

Answer 6

Let's start with the basics. Do you understand what a limit is? Just the rough idea, not the formal definition.

Answer 7

I'm right there with you @Loser66 :P

@1krystibrea your notion of a limit is ... well ... not accurate.

The limit of a function is the value that the function appears to be approaching or converging to.

If I gave you a function like the one drawn below, then asked what the limit was as \(x\to c\), then you can tell me that the function is approaching whatever value the function takes on at \(x=c\). This function has no breaks or jumps - it's continuous at that point, so the limit exists at that point.

Make sense so far?