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

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

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

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

2

Solution steps

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

Divide by highest denominator power:

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

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

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

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

= \frac{4}{2}

Simplify

= 2

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