Evaluate the following limits. \lim_{x\to\infty}(2+\frac{4}{x})^{2x}

Burhan Hopper 2021-10-29 Answered
Evaluate the following limits.
limx(2+4x)2x
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

Expert Answer

comentezq
Answered 2021-10-30 Author has 106 answers
Given:
limx(2+4x)2x
Calculation:
limx(2+4x)2x if we substitute limit x in this we get indeterminate form 2
Let's define y=(2+4x)2x
And take the log on both side and we will do some simplification
lny=ln(2+4x)2x
And take the log on both side and we will do some simplification
lny=ln(2+4x)2x
lny=2xln(2+4x)
lny=ln(2+4x)12x
Taking limit x on both side
limx[lny]=ln(2+4x)12x
limx[lny]=ln(2+4)12
limx[lny]=ln(2+0)0=ln(2)0=
We know that
t=elny
This means we can do original limit as follow
limx(2+4x)2x=limx[y]=limxelny=elimx[lny]e=
Therefore limx(2+4x)2x=
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