What is the limit as x approaches infinity of (2x-4)/(7x+6) ?

The limit as x approaches infinity of (2x-4)/(7x+6) is 2/7

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limit as x approaches infinity of (2x-4)/(7x+6)

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

\frac{2}{7}

Decimal Notation

0.28571 \dots

Solution steps

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

Divide by highest denominator power:

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

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

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

x \to \infty lim (7 + \frac{6}{x}) = 7

= \frac{2}{7}

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

x \to 0 lim (\frac{sin ( 16 x )}{x})

x \to 0 lim (6^{x} - 3^{x})

x \to - \infty lim (b^{x})

x \to 1 + lim (x^{\frac{1}{l n ( x )}})

What is the limit as x approaches infinity of (2x-4)/(7x+6) ?
The limit as x approaches infinity of (2x-4)/(7x+6) is 2/7