Lim x→inf text book example confusing step

  • Thread starter cambo86
  • Start date
  • #1
25
0

Main Question or Discussion Point

I was hoping someone could clarify a step of an example in my calculus textbook.

lim x→∞ (√(2*x2+1))/(3*x-5) = lim x→∞ (√(2+(1/x2)))/(3-(5/x)), (since √x2=x for x>0)

The description for the step says to divide numerator and denominator by x.

I understand to divide top and bottom of a rational function by the xn where n is the highest power of x that occurs in the denominator in this situation but I don't understand how the numerators equate in this equation.
 

Answers and Replies

  • #2
Stephen Tashi
Science Advisor
6,927
1,182
For x > 0, (1/x) sqrt( 2x^2 + 1) = sqrt(1/x^2) sqrt(2x^2 + 1) = sqrt( (1/x^2)(2x^2 + 1) )
 

Related Threads for: Lim x→inf text book example confusing step

  • Last Post
Replies
14
Views
2K
Replies
1
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
4
Views
7K
Replies
4
Views
1K
Replies
7
Views
15K
Replies
1
Views
2K
Top