Find the asymptotes of f:R rightarrow R, f(x)= root(3)(ex−e2x+e4xln2(1+e−x)). I found that y=0 is an asymptote when x rightarrow −infinity, but how do I calculate limx rightarrow infinity f(x) ?

Braylon Lester 2022-07-23 Answered
Find the asymptotes
Find the asymptotes of f : R R , f ( x ) = e x e 2 x + e 4 x ln 2 ( 1 + e x ) 3 .
I found that y=0 is an asymptote when x , but how do I calculate lim x f ( x ) ?
You can still ask an expert for help

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 (1)

Brendon Bentley
Answered 2022-07-24 Author has 11 answers
Let see what happens when x . We have ln ( 1 + y ) = y y 2 2 + y 3 3 + O ( y 4 ) as y 0 hence
f ( x ) = ( e x e 2 x + e 4 x ( e x e 2 x 2 + e 3 x 3 + O ( e 4 x ) ) 2 ) 1 / 3
that is
f ( x ) = ( e x e 2 x + e 4 x ( e 2 x e 3 x + 11 12 e 4 x + O ( e 5 x ) ) ) 1 / 3
therefore
f ( x ) = ( 11 12 + O ( e x ) ) 1 / 3 .
In particular,
lim x f ( x ) = ( 11 12 ) 1 / 3 .
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

New questions