Question

limit of f of x as x approaches 5 where f of x equals 5 minus x when x is less than 5, 8 when x equals 5, and x plus 3 when x is greater than 5

Answer 1

Find the indicated limit, if it exists.

Answer 2

if you need to see the choices it's:
0

8

3

The limit does not exist.

Answer 3

I got 0

Answer 4

Is this info right?
\[f(x)=\begin{cases}5-x&\text{for }x<5\\
8&\text{for }x=5\\
x+3&\text{for }x>5\end{cases}\]
Find
\[\large\lim_{x\to5}f(x)\]

Answer 5

yes

Answer 6

To see if the limit exists at all, you have to check the limits from both sides. If you have
\[\large\lim_{x\to5^-}f(x)=\lim_{x\to5^+}f(x)\]
then the limit exists, and
\[\large\lim_{x\to5}f(x)\]
is the actual limit.

To check the one-sided limits, you have to use the appropriate functions. For \(x\to5^-\), you use the function defined for values of \(x\) to the left of 5, or \(x<5\). For \(x\to5^+\), you use the function defined for \(x>5\):
\[\large\lim_{x\to5^-}f(x)=\lim_{x\to5^-}(5-x)\\
\large\lim_{x\to5^+}f(x)=\lim_{x\to5^+}(x+3)\]

Answer 7

THIS MAKES SO MUCH MORE SENSE