Saturday

January 31, 2015

January 31, 2015

Posted by **Nathan** on Tuesday, October 22, 2013 at 12:43pm.

- Calculus -
**Count Iblis**, Tuesday, October 22, 2013 at 4:51pmsqrt(x^2+6x+3) =

x sqrt(1 + 6/x + 3/x^2)

Using the series expansion:

(1+y)^p = 1 + p y + p (p-1)/2 y^2 + ...

for p = 1/2 gives:

sqrt(1 + 6/x + 3/x^2) = 1 + 3/x +

O(1/x^2)

Where the O(1/x^2) means that there exists an R and a constant c such that for x larger than R, the difference between the square root and (1+3/x) becomes less than c/x^2.

We then have:

x sqrt(1 + 6/x + 3/x^2) - x =

3 + O(1/x)

This means that the limit for x to infinity is 3.

**Answer this Question**

**Related Questions**

calculus - if i define the function f(x)= x^3-x^2-3x-1 and h(x) = f(x)/g(x), ...

AP Calculus - if i define the function f(x)= x^3-x^2-3x-1 and h(x) = f(x)/g(x), ...

Calculus, please check my answers! - 1. Evaluate: lim x->infinity(x^4-7x+9)/(...

Calculus help, please! - 1. Evaluate: lim x->infinity(x^4-7x+9)/(4+5x+x^3) 0...

calculus - evaluate lim of x as it approaches infinity for sqrt of x^2 -1/2x+1

Calculus - Show that limit as n approaches infinity of (1+x/n)^n=e^x for any x&...

Check my CALCULUS work, please! :) - Question 1. lim h->0(sqrt 49+h-7)/h = ...

Calculus - Show that limit as n approaches infinity of (1+x/n)^n=e^x for any x&...

Calculus - Evaluate the following limits. lim as x approaches infinity 6/e^x + 7...

Calculus - Note that pi lim arctan(x ) = ---- x -> +oo 2 Now evaluate / pi \ ...