Question

Discuss the continuity of the function f, where f is defined by

Answer 1

What do you think?

Answer 2

there is 1,3&10 how am i supposed to proceed ?

Answer 3

You have to consider only the points x=1 and x=3. Start with 1.

Answer 4

ok

Answer 5

God, she's so cute!

Answer 6

x tends to 1^+ & 1^- ?

Answer 7

Yeah, and f(1).

Answer 8

If you find that any two of them are different, you don't need to find the third.

Answer 9

That's enough to prove discontinuity.

Answer 10

\[\lim_{x \rightarrow 1^+}f(x)=4\]\[\lim_{x \rightarrow 1^-}=3\]

Answer 11

*f(x)

Answer 12

Conclusion?

Answer 13

discontinuos at 1

Answer 14

Aren't you smart?

Answer 15

lol

Answer 16

what about 10?

Answer 17

Do the same with the point x=3, and you're done!

Answer 18

Left Hand Limit and Right hand Limit of f(x) at points 1 and 3 are not equal and so these two are points of discontinuity of f(x)

Answer 19

discontinuous at 3

Answer 20

The function doesn't change around 10. So you don't need to study the function at that point.

Answer 21

Mr.Math is right with his arguement

Answer 22

But if you want to, you can easily prove that the right hand limit is the same as the left hand as x ->10 , and they are the same as f(10).

Answer 23

so its continuous at 10 ?

Answer 24

Yep! Can you prove it?

Answer 25

yeah

Answer 26

We cannot tell that exactly Mr.Math

Answer 27

Show me!

Answer 28

Oh wait!

Answer 29

The function is only defined from [0,10]. This is the domain of your function, so there's no such limit as \(10^+\).

Answer 30

And so we cannot discuss the continuity at this point

Answer 31

Oh Okay !

Answer 32

Atchyut is right!

Answer 33

Ok ThankYou Mr.Math & Atchyut

Answer 34

Glad to help!

Answer 35

Welcome