What is the limit as x approaches-infinity of ((x^{-1}+x^{-4}))/(x^{-2)-x^{-3}} ?

The limit as x approaches-infinity of ((x^{-1}+x^{-4}))/(x^{-2)-x^{-3}} is -infinity

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limit as x approaches-infinity of ((x^{-1}+x^{-4}))/(x^{-2)-x^{-3}}

x \to - \infty lim (\frac{( x ^{- 1} + x ^{- 4} )}{x ^{- 2} - x ^{- 3}})

- \infty

Solution steps

x \to - \infty lim (\frac{x ^{- 1} + x ^{- 4}}{x ^{- 2} - x ^{- 3}})

Divide by

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

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

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

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

= \frac{- \infty}{1}

Apply Infinity Property:

\frac{- \infty}{c} = - \infty

= - \infty

\int sin (ln (9 x)) d x

\frac{d y}{d x} + 2 y = 5

ln (2 - x^{2} + 2 x^{4})

y^{^{'}} = 2 cos (t) + \frac{y}{2}

x e^{2 x}

What is the limit as x approaches-infinity of ((x^{-1}+x^{-4}))/(x^{-2)-x^{-3}} ?
The limit as x approaches-infinity of ((x^{-1}+x^{-4}))/(x^{-2)-x^{-3}} is -infinity