Find the indicated limit, if it exists.

limit of f of x as x approaches 8 where f of x equals x plus 10 when x is less than 8 and f of x equals 10 minus x when x is greater than or equal to 8

Question

Find the indicated limit, if it exists. 

limit of f of x as x approaches 8 where f of x equals x plus 10 when x is less than 8 and f of x equals 10 minus x when x is greater than or equal to 8

anonymous · Answer

x+10   x less than 8
10-x       x greater than or equal to 8

ganeshie8 · Answer

hey you should start using latex

anonymous · Answer

i have a few questions like this and really want to know how to solve problems like these

anonymous · Answer

latex?

ganeshie8 · Answer

$$f(x) = \left\{\begin{array}{} x+10&:& x \lt 8 \10-x&:&x\ge 8\end{array}\right.$$

like this ?

anonymous · Answer

yes

ganeshie8 · Answer

you want to find  $\lim\limits_{x\to 8} f(x)$

anonymous · Answer

but it has lim with x-->8 under it

anonymous · Answer

You have to check if f is continuous at 8 and -8

ganeshie8 · Answer

we say the limit exists  if you converge to the same value from both left and right sides of 8

ganeshie8 · Answer

plugin x=8 into both the given pieces of function
the limit exists if you get same value

anonymous · Answer

so 18   x less than 8
and 2     x greater than or equal to 8

anonymous · Answer

they are both false

anonymous · Answer

Well they have to equal otherwise the limit does not exist

anonymous · Answer

by equalling each other you mean like getting 18 and 18 when I plug in the 8

ganeshie8 · Answer

yes

anonymous · Answer

oh okay thankssss aton !

anonymous · Answer

so for Find the indicated limit, if it exists. 

limit of f of x as x approaches 0 where f of x equals 5 x minus 9 when x is less than 0 and the absolute value of the quantity 2 minus x when x is greater than or equal to 0
the limit would not exist right?

anonymous · Answer

@ganeshie8

anonymous · Answer

i have gotten that for all my answers in my work

ganeshie8 · Answer

yes limit does not exist because the left and right limits converge to different values. graph makes it easy to see http://gyazo.com/e148f280b022d5186dc7258c1e017731

anonymous · Answer

Oh okay cause out of my 5 hw questions I have gotten so

anonymous · Answer

thanks again!

ganeshie8 · Answer

Notice as you approach 8 from left, the function goes to 18
but when you approach 8 from right, the function goes to 2

they dont converge to same value so we say  $\lim\limits_{x\to 8} f(x) = \text{Does Not Exist}$