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

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

Popular >

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

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

1

Solution steps

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

Simplify

\frac{x ^{2} + 2}{x - 1} - x : \frac{x + 2}{x - 1}

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

Divide by highest denominator power:

\frac{1 + \frac{2}{x}}{1 - \frac{1}{x}}

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

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

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

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

x \to \infty lim (1 - \frac{1}{x}) = 1

= \frac{1}{1}

Simplify

= 1

x \to 0 - lim (x^{2} e^{- \frac{1}{x ^{2}}})

x \to 0 lim (\frac{5 x}{1 - cos ( x )})

x \to 0 lim (\frac{3}{3 x + 4 + 4})

n \to \infty lim (\frac{( 10 - 3 n ) n !}{( n + 1 ) ! - ( n - 1 ) !})

x \to 5 lim (\frac{11}{x ^{2} - 25})

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