the point $z =0$ is choose the correct option












0












$begingroup$


for the function $$f(z) = sinleft(frac{1}{cosfrac{1}{z}}right)$$, the point $z =0$ is



choose the correct option



$1)$ removable singularity



$2) $ pole



$3)$ an essential singularity



$4)$ a non-isolated singularity



My attempt : option 4) will correct i thinks its will have non-isolated singularity because limit of singularity are $dfrac{2}{pi}, dfrac{2}{3pi}, dfrac{2}{5pi}, ldots$.



is its true ?






complex-analysis







share|cite|improve this question











$endgroup$








  • 1




    $begingroup$
    Correct answer. Indeed $z=0$ is not an isolated singularity.
    $endgroup$
    – Yiorgos S. Smyrlis
    Jan 1 at 20:43










  • $begingroup$
    @YiorgosS.Smyrlis thanks'
    $endgroup$
    – jasmine
    Jan 1 at 21:08
















0












$begingroup$


for the function $$f(z) = sinleft(frac{1}{cosfrac{1}{z}}right)$$, the point $z =0$ is



choose the correct option



$1)$ removable singularity



$2) $ pole



$3)$ an essential singularity



$4)$ a non-isolated singularity



My attempt : option 4) will correct i thinks its will have non-isolated singularity because limit of singularity are $dfrac{2}{pi}, dfrac{2}{3pi}, dfrac{2}{5pi}, ldots$.



is its true ?






complex-analysis







share|cite|improve this question











$endgroup$








  • 1




    $begingroup$
    Correct answer. Indeed $z=0$ is not an isolated singularity.
    $endgroup$
    – Yiorgos S. Smyrlis
    Jan 1 at 20:43










  • $begingroup$
    @YiorgosS.Smyrlis thanks'
    $endgroup$
    – jasmine
    Jan 1 at 21:08














0












0








0


1



$begingroup$


for the function $$f(z) = sinleft(frac{1}{cosfrac{1}{z}}right)$$, the point $z =0$ is



choose the correct option



$1)$ removable singularity



$2) $ pole



$3)$ an essential singularity



$4)$ a non-isolated singularity



My attempt : option 4) will correct i thinks its will have non-isolated singularity because limit of singularity are $dfrac{2}{pi}, dfrac{2}{3pi}, dfrac{2}{5pi}, ldots$.



is its true ?






complex-analysis







share|cite|improve this question











$endgroup$




for the function $$f(z) = sinleft(frac{1}{cosfrac{1}{z}}right)$$, the point $z =0$ is



choose the correct option



$1)$ removable singularity



$2) $ pole



$3)$ an essential singularity



$4)$ a non-isolated singularity



My attempt : option 4) will correct i thinks its will have non-isolated singularity because limit of singularity are $dfrac{2}{pi}, dfrac{2}{3pi}, dfrac{2}{5pi}, ldots$.



is its true ?






complex-analysis




complex-analysis






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Jan 1 at 20:39









Dando18

4,66741235




4,66741235










asked Jan 1 at 20:02









jasminejasmine

1,650416




1,650416








  • 1




    $begingroup$
    Correct answer. Indeed $z=0$ is not an isolated singularity.
    $endgroup$
    – Yiorgos S. Smyrlis
    Jan 1 at 20:43










  • $begingroup$
    @YiorgosS.Smyrlis thanks'
    $endgroup$
    – jasmine
    Jan 1 at 21:08














  • 1




    $begingroup$
    Correct answer. Indeed $z=0$ is not an isolated singularity.
    $endgroup$
    – Yiorgos S. Smyrlis
    Jan 1 at 20:43










  • $begingroup$
    @YiorgosS.Smyrlis thanks'
    $endgroup$
    – jasmine
    Jan 1 at 21:08








1




1




$begingroup$
Correct answer. Indeed $z=0$ is not an isolated singularity.
$endgroup$
– Yiorgos S. Smyrlis
Jan 1 at 20:43




$begingroup$
Correct answer. Indeed $z=0$ is not an isolated singularity.
$endgroup$
– Yiorgos S. Smyrlis
Jan 1 at 20:43












$begingroup$
@YiorgosS.Smyrlis thanks'
$endgroup$
– jasmine
Jan 1 at 21:08




$begingroup$
@YiorgosS.Smyrlis thanks'
$endgroup$
– jasmine
Jan 1 at 21:08










0






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