What is the limit as x approaches infinity of (3sqrt(x)+x^{-6})/(4x-4) ?

The limit as x approaches infinity of (3sqrt(x)+x^{-6})/(4x-4) is 0

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limit as x approaches infinity of (3sqrt(x)+x^{-6})/(4x-4)

x \to \infty lim (\frac{3 x + x ^{- 6}}{4 x - 4})

0

Solution steps

x \to \infty lim (\frac{3 x + x ^{- 6}}{4 x - 4})

Divide by highest denominator power:

\frac{\frac{3}{x} + \frac{1}{x ^{7}}}{4 - \frac{4}{x}}

= x \to \infty lim (\frac{\frac{3}{x} + \frac{1}{x ^{7}}}{4 - \frac{4}{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} ( \frac{3}{x} + \frac{1}{x ^{7}} )}{lim _{x \to \infty} ( 4 - \frac{4}{x} )}

x \to \infty lim (\frac{3}{x} + \frac{1}{x ^{7}}) = 0

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

= \frac{0}{4}

Apply rule

\frac{0}{a} = 0, a \neq = 0

= 0

x \to 0 lim (x^{- 3} sin (3 x) + x^{- 2} a + b)

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

x \to 0 lim (\frac{( 9 ^{x} - 4 ^{x} )}{x})

x \to 2 lim (4 (x - 4) (x - 2))

x \to \infty lim (x - 7)

What is the limit as x approaches infinity of (3sqrt(x)+x^{-6})/(4x-4) ?
The limit as x approaches infinity of (3sqrt(x)+x^{-6})/(4x-4) is 0