Using L'Hospital's Rule on $cos (2x)^frac 1 x^2.$ [closed] The 2019 Stack Overflow Developer Survey Results Are InLimit of square root without L'Hopital's rule.Evaluate the limit $lim_x to 0fracsqrt1+xsinx-sqrtcos2xtan^2fracx2$Limits without L'Hopitals RuleComputing $lim_xto 0frac1x(1-e^alpha x)$ using l'Hospital's ruleCorrect use of L'Hospital's rule?Find $lim_x to 0fraccos 2x-1cos x-1$ without L'Hopital's rule.How could I calculate this limit without using L'Hopital's Rule $lim_xrightarrow0 frace^x-1sin(2x)$?Avoiding circular logic using L'Hospital's ruleHow to evaluate $lim _xto 0frac5-5cosleft(2xright)+sinleft(4xright)x$ without using L'Hospital's rule?Limit and L'hopital's Rule

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Using L'Hospital's Rule on $cos (2x)^frac 1 x^2.$ [closed]



The 2019 Stack Overflow Developer Survey Results Are InLimit of square root without L'Hopital's rule.Evaluate the limit $lim_x to 0fracsqrt1+xsinx-sqrtcos2xtan^2fracx2$Limits without L'Hopitals RuleComputing $lim_xto 0frac1x(1-e^alpha x)$ using l'Hospital's ruleCorrect use of L'Hospital's rule?Find $lim_x to 0fraccos 2x-1cos x-1$ without L'Hopital's rule.How could I calculate this limit without using L'Hopital's Rule $lim_xrightarrow0 frace^x-1sin(2x)$?Avoiding circular logic using L'Hospital's ruleHow to evaluate $lim _xto 0frac5-5cosleft(2xright)+sinleft(4xright)x$ without using L'Hospital's rule?Limit and L'hopital's Rule










-3












$begingroup$


How might one evaluate the following limit using L'Hopital's Rule:$$lim_xrightarrow0cos(2x)^frac1x^2$$










share|cite|improve this question











$endgroup$



closed as off-topic by RRL, Eevee Trainer, mrtaurho, Cesareo, Javi Apr 1 at 10:33


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – RRL, Eevee Trainer, mrtaurho, Cesareo, Javi
If this question can be reworded to fit the rules in the help center, please edit the question.











  • 1




    $begingroup$
    What have you tried?
    $endgroup$
    – Kezer
    Mar 30 at 9:53










  • $begingroup$
    Arrived at $e^-2$ using $e^lim_xrightarrow0 fracln(cos(2x))x^2$
    $endgroup$
    – Ali Lodhi
    Mar 30 at 9:57
















-3












$begingroup$


How might one evaluate the following limit using L'Hopital's Rule:$$lim_xrightarrow0cos(2x)^frac1x^2$$










share|cite|improve this question











$endgroup$



closed as off-topic by RRL, Eevee Trainer, mrtaurho, Cesareo, Javi Apr 1 at 10:33


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – RRL, Eevee Trainer, mrtaurho, Cesareo, Javi
If this question can be reworded to fit the rules in the help center, please edit the question.











  • 1




    $begingroup$
    What have you tried?
    $endgroup$
    – Kezer
    Mar 30 at 9:53










  • $begingroup$
    Arrived at $e^-2$ using $e^lim_xrightarrow0 fracln(cos(2x))x^2$
    $endgroup$
    – Ali Lodhi
    Mar 30 at 9:57














-3












-3








-3


1



$begingroup$


How might one evaluate the following limit using L'Hopital's Rule:$$lim_xrightarrow0cos(2x)^frac1x^2$$










share|cite|improve this question











$endgroup$




How might one evaluate the following limit using L'Hopital's Rule:$$lim_xrightarrow0cos(2x)^frac1x^2$$







limits analysis






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Mar 30 at 10:19









Bernard

124k741117




124k741117










asked Mar 30 at 9:29









Ali LodhiAli Lodhi

383




383




closed as off-topic by RRL, Eevee Trainer, mrtaurho, Cesareo, Javi Apr 1 at 10:33


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – RRL, Eevee Trainer, mrtaurho, Cesareo, Javi
If this question can be reworded to fit the rules in the help center, please edit the question.







closed as off-topic by RRL, Eevee Trainer, mrtaurho, Cesareo, Javi Apr 1 at 10:33


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – RRL, Eevee Trainer, mrtaurho, Cesareo, Javi
If this question can be reworded to fit the rules in the help center, please edit the question.







  • 1




    $begingroup$
    What have you tried?
    $endgroup$
    – Kezer
    Mar 30 at 9:53










  • $begingroup$
    Arrived at $e^-2$ using $e^lim_xrightarrow0 fracln(cos(2x))x^2$
    $endgroup$
    – Ali Lodhi
    Mar 30 at 9:57













  • 1




    $begingroup$
    What have you tried?
    $endgroup$
    – Kezer
    Mar 30 at 9:53










  • $begingroup$
    Arrived at $e^-2$ using $e^lim_xrightarrow0 fracln(cos(2x))x^2$
    $endgroup$
    – Ali Lodhi
    Mar 30 at 9:57








1




1




$begingroup$
What have you tried?
$endgroup$
– Kezer
Mar 30 at 9:53




$begingroup$
What have you tried?
$endgroup$
– Kezer
Mar 30 at 9:53












$begingroup$
Arrived at $e^-2$ using $e^lim_xrightarrow0 fracln(cos(2x))x^2$
$endgroup$
– Ali Lodhi
Mar 30 at 9:57





$begingroup$
Arrived at $e^-2$ using $e^lim_xrightarrow0 fracln(cos(2x))x^2$
$endgroup$
– Ali Lodhi
Mar 30 at 9:57











2 Answers
2






active

oldest

votes


















0












$begingroup$

Hint: Write $$e^lim_xto 0fracln(cos(2x)x^2$$






share|cite|improve this answer









$endgroup$












  • $begingroup$
    Right, thankyou.
    $endgroup$
    – Ali Lodhi
    Mar 30 at 9:33










  • $begingroup$
    Want you to know the result?
    $endgroup$
    – Dr. Sonnhard Graubner
    Mar 30 at 9:34










  • $begingroup$
    Yes, I want to know the result.
    $endgroup$
    – Ali Lodhi
    Mar 30 at 9:48










  • $begingroup$
    It is $$e^-2$$
    $endgroup$
    – Dr. Sonnhard Graubner
    Mar 30 at 9:51










  • $begingroup$
    Yes, arrived at that. Thank you.
    $endgroup$
    – Ali Lodhi
    Mar 30 at 9:53


















0












$begingroup$

Hint:



$$y=cos(2x)^1/x^2Rightarrow ln y=4fraclncos(2x)(2x)^2\
1-frac1zleqln zleq z-1$$






share|cite|improve this answer









$endgroup$












  • $begingroup$
    Proof of bounds: proofwiki.org/wiki/Bounds_of_Natural_Logarithm
    $endgroup$
    – Jam
    Mar 30 at 9:59

















2 Answers
2






active

oldest

votes








2 Answers
2






active

oldest

votes









active

oldest

votes






active

oldest

votes









0












$begingroup$

Hint: Write $$e^lim_xto 0fracln(cos(2x)x^2$$






share|cite|improve this answer









$endgroup$












  • $begingroup$
    Right, thankyou.
    $endgroup$
    – Ali Lodhi
    Mar 30 at 9:33










  • $begingroup$
    Want you to know the result?
    $endgroup$
    – Dr. Sonnhard Graubner
    Mar 30 at 9:34










  • $begingroup$
    Yes, I want to know the result.
    $endgroup$
    – Ali Lodhi
    Mar 30 at 9:48










  • $begingroup$
    It is $$e^-2$$
    $endgroup$
    – Dr. Sonnhard Graubner
    Mar 30 at 9:51










  • $begingroup$
    Yes, arrived at that. Thank you.
    $endgroup$
    – Ali Lodhi
    Mar 30 at 9:53















0












$begingroup$

Hint: Write $$e^lim_xto 0fracln(cos(2x)x^2$$






share|cite|improve this answer









$endgroup$












  • $begingroup$
    Right, thankyou.
    $endgroup$
    – Ali Lodhi
    Mar 30 at 9:33










  • $begingroup$
    Want you to know the result?
    $endgroup$
    – Dr. Sonnhard Graubner
    Mar 30 at 9:34










  • $begingroup$
    Yes, I want to know the result.
    $endgroup$
    – Ali Lodhi
    Mar 30 at 9:48










  • $begingroup$
    It is $$e^-2$$
    $endgroup$
    – Dr. Sonnhard Graubner
    Mar 30 at 9:51










  • $begingroup$
    Yes, arrived at that. Thank you.
    $endgroup$
    – Ali Lodhi
    Mar 30 at 9:53













0












0








0





$begingroup$

Hint: Write $$e^lim_xto 0fracln(cos(2x)x^2$$






share|cite|improve this answer









$endgroup$



Hint: Write $$e^lim_xto 0fracln(cos(2x)x^2$$







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Mar 30 at 9:31









Dr. Sonnhard GraubnerDr. Sonnhard Graubner

78.8k42867




78.8k42867











  • $begingroup$
    Right, thankyou.
    $endgroup$
    – Ali Lodhi
    Mar 30 at 9:33










  • $begingroup$
    Want you to know the result?
    $endgroup$
    – Dr. Sonnhard Graubner
    Mar 30 at 9:34










  • $begingroup$
    Yes, I want to know the result.
    $endgroup$
    – Ali Lodhi
    Mar 30 at 9:48










  • $begingroup$
    It is $$e^-2$$
    $endgroup$
    – Dr. Sonnhard Graubner
    Mar 30 at 9:51










  • $begingroup$
    Yes, arrived at that. Thank you.
    $endgroup$
    – Ali Lodhi
    Mar 30 at 9:53
















  • $begingroup$
    Right, thankyou.
    $endgroup$
    – Ali Lodhi
    Mar 30 at 9:33










  • $begingroup$
    Want you to know the result?
    $endgroup$
    – Dr. Sonnhard Graubner
    Mar 30 at 9:34










  • $begingroup$
    Yes, I want to know the result.
    $endgroup$
    – Ali Lodhi
    Mar 30 at 9:48










  • $begingroup$
    It is $$e^-2$$
    $endgroup$
    – Dr. Sonnhard Graubner
    Mar 30 at 9:51










  • $begingroup$
    Yes, arrived at that. Thank you.
    $endgroup$
    – Ali Lodhi
    Mar 30 at 9:53















$begingroup$
Right, thankyou.
$endgroup$
– Ali Lodhi
Mar 30 at 9:33




$begingroup$
Right, thankyou.
$endgroup$
– Ali Lodhi
Mar 30 at 9:33












$begingroup$
Want you to know the result?
$endgroup$
– Dr. Sonnhard Graubner
Mar 30 at 9:34




$begingroup$
Want you to know the result?
$endgroup$
– Dr. Sonnhard Graubner
Mar 30 at 9:34












$begingroup$
Yes, I want to know the result.
$endgroup$
– Ali Lodhi
Mar 30 at 9:48




$begingroup$
Yes, I want to know the result.
$endgroup$
– Ali Lodhi
Mar 30 at 9:48












$begingroup$
It is $$e^-2$$
$endgroup$
– Dr. Sonnhard Graubner
Mar 30 at 9:51




$begingroup$
It is $$e^-2$$
$endgroup$
– Dr. Sonnhard Graubner
Mar 30 at 9:51












$begingroup$
Yes, arrived at that. Thank you.
$endgroup$
– Ali Lodhi
Mar 30 at 9:53




$begingroup$
Yes, arrived at that. Thank you.
$endgroup$
– Ali Lodhi
Mar 30 at 9:53











0












$begingroup$

Hint:



$$y=cos(2x)^1/x^2Rightarrow ln y=4fraclncos(2x)(2x)^2\
1-frac1zleqln zleq z-1$$






share|cite|improve this answer









$endgroup$












  • $begingroup$
    Proof of bounds: proofwiki.org/wiki/Bounds_of_Natural_Logarithm
    $endgroup$
    – Jam
    Mar 30 at 9:59















0












$begingroup$

Hint:



$$y=cos(2x)^1/x^2Rightarrow ln y=4fraclncos(2x)(2x)^2\
1-frac1zleqln zleq z-1$$






share|cite|improve this answer









$endgroup$












  • $begingroup$
    Proof of bounds: proofwiki.org/wiki/Bounds_of_Natural_Logarithm
    $endgroup$
    – Jam
    Mar 30 at 9:59













0












0








0





$begingroup$

Hint:



$$y=cos(2x)^1/x^2Rightarrow ln y=4fraclncos(2x)(2x)^2\
1-frac1zleqln zleq z-1$$






share|cite|improve this answer









$endgroup$



Hint:



$$y=cos(2x)^1/x^2Rightarrow ln y=4fraclncos(2x)(2x)^2\
1-frac1zleqln zleq z-1$$







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Mar 30 at 9:58









JamJam

5,01921432




5,01921432











  • $begingroup$
    Proof of bounds: proofwiki.org/wiki/Bounds_of_Natural_Logarithm
    $endgroup$
    – Jam
    Mar 30 at 9:59
















  • $begingroup$
    Proof of bounds: proofwiki.org/wiki/Bounds_of_Natural_Logarithm
    $endgroup$
    – Jam
    Mar 30 at 9:59















$begingroup$
Proof of bounds: proofwiki.org/wiki/Bounds_of_Natural_Logarithm
$endgroup$
– Jam
Mar 30 at 9:59




$begingroup$
Proof of bounds: proofwiki.org/wiki/Bounds_of_Natural_Logarithm
$endgroup$
– Jam
Mar 30 at 9:59



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