Solve limit <munder> <mo movablelimits="true" form="prefix">lim <mrow class="MJX-TeXAt

dokezwa17 2022-05-19 Answered
Solve limit lim x 0 x sin ( x ) ( x sin ( x ) ) 3 / 2
You can still ask an expert for help

Want to know more about Limits and continuity?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (2)

Julien Carrillo
Answered 2022-05-20 Author has 13 answers
You have with Taylor series around 0 :
sin ( x ) = x x 3 6 + o ( x 3 )
lim x 0 x sin ( x ) ( x sin ( x ) ) 3 / 2 = lim x 0 x x + x 3 6 + o ( x 3 ) ( x ( x + o ( x ) ) 3 / 2 = lim x 0 x 3 6 + o ( x 3 ) x 3 + o ( x 3 ) = 1 6
Not exactly what you’re looking for?
Ask My Question
Mackenzie Rios
Answered 2022-05-21 Author has 4 answers
For x 0 we have ( sin x ) 3 / 2 x 3 / 2 and so
x sin x ( x sin x ) 3 / 2 x 3 3 ! x 3 / 2 ( x ) 3 / 2 = 1 6
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more