Question

if f(0)=k
f(x)=(x^2-x)/(2x)
and f is discontinuous at x=0, then k =
A)-1 B)-1/s C)0 D)1/s E)1

can someone explain how to solve this?

Answer 1

So wait a minute
are you saying f(x)= k if x=0 and (x^2-x)/(2x) if x doesn't equal 0
and you have the question if f is discontinuous at x=0, then k=?

Answer 2

what is s?

Answer 3

is s, two?

Answer 4

And are you sure we don't want to find k so that f is continuous at x=0?

Answer 5

Because that question would make more sense?

Answer 6

uhm let me send a picture of what it looks like

Answer 7

trick is to try to reduce that one fraction first

Answer 8

so wouldn't it be x(x-1)/2x?

Answer 9

then cancel a factor x on top and bottom

Answer 10

this is what we want
\[\lim_{x \rightarrow 0}\frac{x-1}{2} =k\]

Answer 11

recall that we want \[\lim_{x \rightarrow 0}f(x)=f(0) \]
if we have that then it is continuous at x=0

Answer 12

s=2

Answer 13

where is the dolphin? Are you still there?

Answer 14

yes I'm here

Answer 15

so then how would we find k?

Answer 16

\[\lim_{x \rightarrow 0}\frac{x-1}{2} =k\]
Does this equation make any sense to you?

Answer 17

\[\lim_{x \rightarrow 0}f(x)=f(0) \\ \lim_{x \rightarrow 0}\frac{x-1}{2}=f(0) \\ \lim_{x \rightarrow 0}\frac{x-1}{2}=k\]

Answer 18

find that limit and you are done because k is equal to what limit you get there

Answer 19

oh so then i would just plug in zero and get -1/2 right?

Answer 20

yea

Answer 21

the function (x-1)/2 is continuous at x=0 so you can just plug in 0 for x

Answer 22

that is how uncle and i already knew what you meant by s

Answer 23

lol

Answer 24

s had to be two in order for there to be an answer

Answer 25

oh lol okay. I see. well thank you very much. You helped lots !

Answer 26

np