What is the limit as x approaches-infinity of sqrt(x^2-2x+1)-x ?

The limit as x approaches-infinity of sqrt(x^2-2x+1)-x is infinity

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limit as x approaches-infinity of sqrt(x^2-2x+1)-x

x \to - \infty lim (x^{2} - 2 x + 1 - x)

\infty

Solution steps

x \to - \infty lim (x^{2} - 2 x + 1 - x)

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

= x \to - \infty lim (x^{2} - 2 x + 1) - x \to - \infty lim (x)

x \to - \infty lim (x^{2} - 2 x + 1) = \infty

x \to - \infty lim (x) = - \infty

= \infty - (- \infty)

Apply Infinity Property:

\infty + \infty = \infty

= \infty

\int \frac{13}{( x ^{2} - 1 ) ^{2}} d x

\frac{\partial}{\partial y} (tan (x^{2} + y^{2}))

f (x) = \frac{1 - sin ( x )}{1 + sin ( x )}

\int \frac{1}{x + 4} d x

f (x) = x - a

What is the limit as x approaches-infinity of sqrt(x^2-2x+1)-x ?
The limit as x approaches-infinity of sqrt(x^2-2x+1)-x is infinity