Find the following limit: lim_{xrightarrow0}frac{xe^x}{e^{3x}-1}

ankarskogC 2021-03-04 Answered
Find the following limit:
limx0xexe3x1
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

casincal
Answered 2021-03-05 Author has 82 answers
Given:
limx0xexe3x1
Now Applying limits:
limx0xexe3x1=0(e0)e3(0)1=00
Hence it gives indeterminate form 00
Now by L-Hospital Rule:
limx0[ddx(xex)ddx(e3x1)]=limx0[xex+ex3e3x]
=[0(e0)+e03e3(0)]
[=13]
Hence,
limx0xexe3x1=13
Not exactly what you’re looking for?
Ask My Question
Jeffrey Jordon
Answered 2022-04-01 Author has 2087 answers

Expert Community at Your Service

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