lim x->infinity ((sqrt(x^2+5))-(sqrt(x^2+3)))

Expert Answers

An illustration of the letter 'A' in a speech bubbles

The answer is Zero, but I suspect you knew that before you posed the question.  

We can simplify this problem without resorting to calculus.  Recall that

lim x->infty(f(x) + g(x)) = lim x->infty(f(x)) + lim x->infty(g(x))

Now it is easy to see that sqrt(x^2+5) approaches infinity with x, and so does sqrt(x^2+3).  Since the limits are equal, the difference of the limits is zero.

Approved by eNotes Editorial Team

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial