Question

Find the indicated limit, if it exists.

limit of f of x as x approaches 9 where f of x equals x plus 9 when x is less than 9 and f of x equals 9 minus x when x is greater than or equal to 9

Answer 1

I don't quite understand how they want me to solve this

Answer 2

The limit will exist is its value when x approaches from either side,
less than 9 or greater than 9,
is SAME!

so can you tell me whats the limits value when x<9 ?

Answer 3

I honestly don't know

Answer 4

is it everything less than 9?

Answer 5

do you know how to evaluate limits?
like this one?
\(\lim \limits_{x\to 9}x+9 =.. ?\)

you know what to do?

Answer 6

yah

Answer 7

what ?

Answer 8

its 18 right?

Answer 9

the limit to x+9 is 18

Answer 10

as the values of x approach nine

Answer 11

yes! that was when x<9
so you just plug in x = 9
whenever you can.

similarly whats
\( \lim \limits_{x \to 9 }
9-x = .. ?\)

Answer 12

that would be zero?

Answer 13

correct,
now are these same?

Answer 14

you are plugging in 9 into the x values to get closer to zero?

Answer 15

we are plugging in x= 9 in the function, because x approaches 9

when x<9, we got the limit as 18,
when x is > or = 9, we got the limit as 0

its like a sudden spike!