Question

Find the indicated limit, if it exists.

Answer 1

limx→9f(x),f(x)=[x+927−xx<9x≥9]

Answer 2

have you tried a similar question before ?

Answer 3

No.

Answer 4

I'm not familiar with matrices in this type of problem

Answer 5

Know about left hand and right hand limits?

Answer 6

Yeah, I guess

Answer 7

so could you find those limits for f(x) ?

Answer 8

I don't really know how to do this with matrices.

Answer 9

IS the limit 18?

Answer 10

its not a matrix :)

its a piecewise function,

when x<9, f(x) = x+9
when x>= 9, f(x) = 27-x

Answer 11

how did you find out that the limit = 18 ?

Answer 12

As x approaches nine, f(x) approaches 18. 9+9=18

Answer 13

Does that make sense, or am I completely wrong?

Answer 14

that makes one-third sense :)

let me explain,

Answer 15

Gladly.

Answer 16

so, we need to find whether x approaches same number when

x<9,
x=9,
x>9

if for all these 3 conditions, f(x) approaches same number,
then you limit exist!
and the limit value = that number.

Answer 17

for x>9,
we use x>=9 function

which is 27-x

so, 27- 9 =18

for x = 9, we use x>=9 again,

which is 27-x = 18

Answer 18

So the limit does exist?

Answer 19

and it is 18

Answer 20

for x<9, we use
x+9 function

so 9+9 = 18

so we indeed get 18 for all 3 conditions!

hence limit exist and is = 18 :)

Answer 21

Thank you.

Answer 22

hope you can try next problem on your own now :)
and welcome ^_^