Question

The function f(x)=(x-4)/absolute(x-4), is defined everywhere except at x=4. If possible, define f(x) at 4 so that it becomes continuous at 4?

Answer 1

1

Answer 2

uve gotta evaluate f(x) as x tends to 4

Answer 3

a) Not possible because there is an infinite discontinuity at the given point.
b) f (4) = 0
c) f (4) = -1
d) Not possible because there is a jump discontinuity at the given point.
e) f (4) = 1

Answer 4

\[\lim_{x \rightarrow 4+}[(x-4)/|x-4|] =\lim_{h \rightarrow 0}[(4+h-4)/|4+h-4|] = h/h = 1\]

Answer 5

wait...no

Answer 6

d

Answer 7

I'm confused

Answer 8

bcoz the LHL is -1

Answer 9

for continuity function must be defined at that point, howz it 1?

Answer 10

we have to evaluate the limit uzma...which is infact nonexistent..as LHL is -1 and RHL is 1

Answer 11

we r to define f so that it is continuous at 4

Answer 12

yeah

Answer 13

so akileez..see the left hand limit at 4 is -1, and the right hand limit is 1, so ur answer is d

Answer 14

for x greater than 4, its 1 and for x less than 4 its -1,

Answer 15

him is right now

Answer 16

ok, I get it! since the left and right cannot equal, there is not point where f(x) will be continuous _ isn't his general for anything over absolutes?

Answer 17

but, why is it a jump disc and not an infinite?

Answer 18

because both the limit values are finite, theyre just not equal to each other

Answer 19

and if they were equal to each other?

Answer 20

for a function to be continuous
L.H.L=R.H.L= value of the function at that point

Answer 21

uzma can you pls write down the calcs that work out the value for the limit form the left and right side pls!