What is the limit as x approaches infinity of (6x^6+x)/(7x^5-2x) ?

The limit as x approaches infinity of (6x^6+x)/(7x^5-2x) is infinity

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limit as x approaches infinity of (6x^6+x)/(7x^5-2x)

x \to \infty lim (\frac{6 x ^{6} + x}{7 x ^{5} - 2 x})

\infty

Solution steps

x \to \infty lim (\frac{6 x ^{6} + x}{7 x ^{5} - 2 x})

Divide by highest denominator power:

\frac{6 x + \frac{1}{x ^{4}}}{7 - \frac{2}{x ^{4}}}

= x \to \infty lim (\frac{6 x + \frac{1}{x ^{4}}}{7 - \frac{2}{x ^{4}}})

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} ( 6 x + \frac{1}{x ^{4}} )}{lim _{x \to \infty} ( 7 - \frac{2}{x ^{4}} )}

x \to \infty lim (6 x + \frac{1}{x ^{4}}) = \infty

x \to \infty lim (7 - \frac{2}{x ^{4}}) = 7

= \frac{\infty}{7}

Apply Infinity Property:

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

= \infty

x \to \infty + lim (\frac{( e ^{x} )}{x})

t \to \infty lim (t e^{t})

x \to 0 lim (\frac{3}{2})

x \to 0 + lim (x^{9} (ln (x))^{2})

x \to 2 + lim (8 - 2 x - x^{2})

What is the limit as x approaches infinity of (6x^6+x)/(7x^5-2x) ?
The limit as x approaches infinity of (6x^6+x)/(7x^5-2x) is infinity