# Math Help - Limits at Infinity

1. ## Limits at Infinity

Lim {x - > ∞ } (x - √x^2 + x)

Evaluate the Limit

2. Originally Posted by valeriegriff
Lim {x - > ∞ } (x - √x^2 + x)

Evaluate the Limit
Either I've missed something or the question is wrong:

$x - \sqrt{x^2} + x = x-x+x = 2x-x = x$

so the limit would be $\infty$

3. Originally Posted by valeriegriff
Lim {x - > ∞ } (x - √x^2 + x)

Evaluate the Limit
$\mathop {\lim }\limits_{x \to \infty } \left( {x - \sqrt {{x^2} + x} } \right) = \mathop {\lim }\limits_{x \to \infty } \frac{{\left( {x - \sqrt {{x^2} + x} } \right)\left( {x + \sqrt {{x^2} + x} } \right)}}
{{x + \sqrt {{x^2} + x} }} =$

$= - \mathop {\lim }\limits_{x \to \infty } \frac{x}
{{x + \sqrt {{x^2} + x} }} = - \mathop {\lim }\limits_{x \to \infty } \frac{1}
{{1 + \sqrt {1 + \frac{1}
{{{x^2}}}} }} = - \frac{1}
{{1 + \sqrt {1 + 0} }} = - \frac{1}
{2}.$