What is the limit as x approaches infinity of (4x^{-1}-2x^{-3})/(3x^{-2)+x^{-5}} ?

The limit as x approaches infinity of (4x^{-1}-2x^{-3})/(3x^{-2)+x^{-5}} is infinity

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limit as x approaches infinity of (4x^{-1}-2x^{-3})/(3x^{-2)+x^{-5}}

x \to \infty lim (\frac{4 x ^{- 1} - 2 x ^{- 3}}{3 x ^{- 2} + x ^{- 5}})

\infty

Solution steps

x \to \infty lim (\frac{4 x ^{- 1} - 2 x ^{- 3}}{3 x ^{- 2} + x ^{- 5}})

Divide by

x^{- 2} : \frac{4 x - \frac{2}{x}}{3 + \frac{1}{x ^{3}}}

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

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

x \to \infty lim (4 x - \frac{2}{x}) = \infty

x \to \infty lim (3 + \frac{1}{x ^{3}}) = 3

= \frac{\infty}{3}

Apply Infinity Property:

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

= \infty

e^{- \frac{t}{2}} - \frac{e ^{- \frac{t}{2}} t}{2}

y = 8 x - 6, (64, 58)

\int_{7}^{9} (x^{2} + 2 x - 5) d x

\int x^{2} e^{4 x} d x

\frac{1}{s ^{2} + 6 s + 25}

What is the limit as x approaches infinity of (4x^{-1}-2x^{-3})/(3x^{-2)+x^{-5}} ?
The limit as x approaches infinity of (4x^{-1}-2x^{-3})/(3x^{-2)+x^{-5}} is infinity