Points of discontinuity and non differentiability of $| sin(pi/x)|$?
$begingroup$
What are the points of discontinuity and non-differentiability of
$| sin(pi/x)|$?
I tried finding out the points of discontinuity for the function but couldn't understand why would a mod function by discontinuous at all...
Plz help me out , also if there are points of non discontinuity please tell how to solve such modulus ques
discontinuous-functions
edited Dec 14 '18 at 5:21
Eevee Trainer
10.2k31742
asked Dec 14 '18 at 5:12
Shivang KohliShivang Kohli
1
$endgroup$
add a comment |
$begingroup$
What are the points of discontinuity and non-differentiability of
$| sin(pi/x)|$?
I tried finding out the points of discontinuity for the function but couldn't understand why would a mod function by discontinuous at all...
Plz help me out , also if there are points of non discontinuity please tell how to solve such modulus ques
discontinuous-functions
edited Dec 14 '18 at 5:21
Eevee Trainer
10.2k31742
asked Dec 14 '18 at 5:12
Shivang KohliShivang Kohli
1
$endgroup$
1
$begingroup$
See math.meta.stackexchange.com/questions/5020 and please avoid plz.
$endgroup$
– Lord Shark the Unknown
Dec 14 '18 at 5:17
$begingroup$
Apologies.. I will keep that in mind from now
$endgroup$
– Shivang Kohli
Dec 14 '18 at 5:46
add a comment |
$begingroup$
What are the points of discontinuity and non-differentiability of
$| sin(pi/x)|$?
I tried finding out the points of discontinuity for the function but couldn't understand why would a mod function by discontinuous at all...
Plz help me out , also if there are points of non discontinuity please tell how to solve such modulus ques
discontinuous-functions
edited Dec 14 '18 at 5:21
Eevee Trainer
10.2k31742
asked Dec 14 '18 at 5:12
Shivang KohliShivang Kohli
1
$endgroup$
What are the points of discontinuity and non-differentiability of
$| sin(pi/x)|$?
I tried finding out the points of discontinuity for the function but couldn't understand why would a mod function by discontinuous at all...
Plz help me out , also if there are points of non discontinuity please tell how to solve such modulus ques
discontinuous-functions
discontinuous-functions
edited Dec 14 '18 at 5:21
Eevee Trainer
10.2k31742
asked Dec 14 '18 at 5:12
Shivang KohliShivang Kohli
1
edited Dec 14 '18 at 5:21
Eevee Trainer
10.2k31742
asked Dec 14 '18 at 5:12
Shivang KohliShivang Kohli
1
edited Dec 14 '18 at 5:21
Eevee Trainer
10.2k31742
edited Dec 14 '18 at 5:21
Eevee Trainer
10.2k31742
edited Dec 14 '18 at 5:21
Eevee Trainer
10.2k31742
10.2k31742
asked Dec 14 '18 at 5:12
Shivang KohliShivang Kohli
1
asked Dec 14 '18 at 5:12
Shivang KohliShivang Kohli
1
asked Dec 14 '18 at 5:12
Shivang KohliShivang Kohli
1
1
1
$begingroup$
See math.meta.stackexchange.com/questions/5020 and please avoid plz.
$endgroup$
– Lord Shark the Unknown
Dec 14 '18 at 5:17
$begingroup$
Apologies.. I will keep that in mind from now
$endgroup$
– Shivang Kohli
Dec 14 '18 at 5:46
add a comment |
1
$begingroup$
See math.meta.stackexchange.com/questions/5020 and please avoid plz.
$endgroup$
– Lord Shark the Unknown
Dec 14 '18 at 5:17
$begingroup$
Apologies.. I will keep that in mind from now
$endgroup$
– Shivang Kohli
Dec 14 '18 at 5:46
1
1
$begingroup$
See math.meta.stackexchange.com/questions/5020 and please avoid plz.
$endgroup$
– Lord Shark the Unknown
Dec 14 '18 at 5:17
$begingroup$
See math.meta.stackexchange.com/questions/5020 and please avoid plz.
$endgroup$
– Lord Shark the Unknown
Dec 14 '18 at 5:17
$begingroup$
Apologies.. I will keep that in mind from now
$endgroup$
– Shivang Kohli
Dec 14 '18 at 5:46
$begingroup$
Apologies.. I will keep that in mind from now
$endgroup$
– Shivang Kohli
Dec 14 '18 at 5:46
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
A discontinuity would be where the function in question does not have a defined value, or those where the function "jumps".
In that light, what would be the places where $f(x) = |sin(pi / x)|$ cannot be evaluated, or where are the jumps? We know $sin(x)$ and $|x|$ are defined for all real $x$ and have no jumps, so the only possibility would be where the argument of the function, $pi/x$, is undefined. In that light, it should be clear as to what the discontinuity of the function is.
A graph of the function will definitely prove useful as well.
As for determining where $f(x)$ is not differentiable, it might be easiest to first graph $f$. It'll have a bunch of a "sharp" points, which, if you remember discussions on differentiability from Calculus I and such classes, will be a sign of not being differentiable there. Finding $f'(x)$ explicitly will also help determine where the function is not differentiable as well, but I think the graphing method is sufficient in this case unless you want a fully-rigorous approach.
answered Dec 14 '18 at 5:20
Eevee TrainerEevee Trainer
10.2k31742
$endgroup$
$begingroup$
Thanx a lot for your help
$endgroup$
– Shivang Kohli
Dec 14 '18 at 5:38
add a comment |
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1 Answer
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oldest
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$begingroup$
A discontinuity would be where the function in question does not have a defined value, or those where the function "jumps".
In that light, what would be the places where $f(x) = |sin(pi / x)|$ cannot be evaluated, or where are the jumps? We know $sin(x)$ and $|x|$ are defined for all real $x$ and have no jumps, so the only possibility would be where the argument of the function, $pi/x$, is undefined. In that light, it should be clear as to what the discontinuity of the function is.
A graph of the function will definitely prove useful as well.
As for determining where $f(x)$ is not differentiable, it might be easiest to first graph $f$. It'll have a bunch of a "sharp" points, which, if you remember discussions on differentiability from Calculus I and such classes, will be a sign of not being differentiable there. Finding $f'(x)$ explicitly will also help determine where the function is not differentiable as well, but I think the graphing method is sufficient in this case unless you want a fully-rigorous approach.
answered Dec 14 '18 at 5:20
Eevee TrainerEevee Trainer
10.2k31742
$endgroup$
$begingroup$
Thanx a lot for your help
$endgroup$
– Shivang Kohli
Dec 14 '18 at 5:38
add a comment |
$begingroup$
A discontinuity would be where the function in question does not have a defined value, or those where the function "jumps".
In that light, what would be the places where $f(x) = |sin(pi / x)|$ cannot be evaluated, or where are the jumps? We know $sin(x)$ and $|x|$ are defined for all real $x$ and have no jumps, so the only possibility would be where the argument of the function, $pi/x$, is undefined. In that light, it should be clear as to what the discontinuity of the function is.
A graph of the function will definitely prove useful as well.
As for determining where $f(x)$ is not differentiable, it might be easiest to first graph $f$. It'll have a bunch of a "sharp" points, which, if you remember discussions on differentiability from Calculus I and such classes, will be a sign of not being differentiable there. Finding $f'(x)$ explicitly will also help determine where the function is not differentiable as well, but I think the graphing method is sufficient in this case unless you want a fully-rigorous approach.
answered Dec 14 '18 at 5:20
Eevee TrainerEevee Trainer
10.2k31742
$endgroup$
$begingroup$
Thanx a lot for your help
$endgroup$
– Shivang Kohli
Dec 14 '18 at 5:38
add a comment |
$begingroup$
A discontinuity would be where the function in question does not have a defined value, or those where the function "jumps".
In that light, what would be the places where $f(x) = |sin(pi / x)|$ cannot be evaluated, or where are the jumps? We know $sin(x)$ and $|x|$ are defined for all real $x$ and have no jumps, so the only possibility would be where the argument of the function, $pi/x$, is undefined. In that light, it should be clear as to what the discontinuity of the function is.
A graph of the function will definitely prove useful as well.
As for determining where $f(x)$ is not differentiable, it might be easiest to first graph $f$. It'll have a bunch of a "sharp" points, which, if you remember discussions on differentiability from Calculus I and such classes, will be a sign of not being differentiable there. Finding $f'(x)$ explicitly will also help determine where the function is not differentiable as well, but I think the graphing method is sufficient in this case unless you want a fully-rigorous approach.
answered Dec 14 '18 at 5:20
Eevee TrainerEevee Trainer
10.2k31742
$endgroup$
A discontinuity would be where the function in question does not have a defined value, or those where the function "jumps".
In that light, what would be the places where $f(x) = |sin(pi / x)|$ cannot be evaluated, or where are the jumps? We know $sin(x)$ and $|x|$ are defined for all real $x$ and have no jumps, so the only possibility would be where the argument of the function, $pi/x$, is undefined. In that light, it should be clear as to what the discontinuity of the function is.
A graph of the function will definitely prove useful as well.
As for determining where $f(x)$ is not differentiable, it might be easiest to first graph $f$. It'll have a bunch of a "sharp" points, which, if you remember discussions on differentiability from Calculus I and such classes, will be a sign of not being differentiable there. Finding $f'(x)$ explicitly will also help determine where the function is not differentiable as well, but I think the graphing method is sufficient in this case unless you want a fully-rigorous approach.
answered Dec 14 '18 at 5:20
Eevee TrainerEevee Trainer
10.2k31742
answered Dec 14 '18 at 5:20
Eevee TrainerEevee Trainer
10.2k31742
answered Dec 14 '18 at 5:20
Eevee TrainerEevee Trainer
10.2k31742
answered Dec 14 '18 at 5:20
Eevee TrainerEevee Trainer
10.2k31742
10.2k31742
$begingroup$
Thanx a lot for your help
$endgroup$
– Shivang Kohli
Dec 14 '18 at 5:38
add a comment |
$begingroup$
Thanx a lot for your help
$endgroup$
– Shivang Kohli
Dec 14 '18 at 5:38
$begingroup$
Thanx a lot for your help
$endgroup$
– Shivang Kohli
Dec 14 '18 at 5:38
$begingroup$
Thanx a lot for your help
$endgroup$
– Shivang Kohli
Dec 14 '18 at 5:38
add a comment |
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1
$begingroup$
See math.meta.stackexchange.com/questions/5020 and please avoid plz.
$endgroup$
– Lord Shark the Unknown
Dec 14 '18 at 5:17
$begingroup$
Apologies.. I will keep that in mind from now
$endgroup$
– Shivang Kohli
Dec 14 '18 at 5:46