Determine the domain of the function and prove that it is continuous on its doma

vazelinahS 2021-10-20 Answered
Determine the domain of the function and prove that it is continuous on its domain using the Laws of Continuity and the facts quoted in this section. f(x)=(x4+1)32
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

nitruraviX
Answered 2021-10-21 Author has 101 answers

Given:
f(x)=(x4+1)32
The function has no undefined points nor domain constraints. Therefore, the is <x<
Interval notation (,)
By law of continuity:
limx(x4+1)32
limxa[f(x)]b=[limxaf(x)}]b
(limx(x4+1))32
Apply Infinity Property: limx±(axn++bx+c)=,a>0 n is even
a=1, n=4
=32
Apply Infinity Property: c=
=
Hence proved
f(x) is continuous in its domain (,)

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