What is the limit as x approaches infinity of (3x+1)/(2x+1) ?

The limit as x approaches infinity of (3x+1)/(2x+1) is 3/2

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limit as x approaches infinity of (3x+1)/(2x+1)

x \to \infty lim (\frac{3 x + 1}{2 x + 1})

\frac{3}{2}

Decimal Notation

1.5

Solution steps

x \to \infty lim (\frac{3 x + 1}{2 x + 1})

Divide by highest denominator power:

\frac{3 + \frac{1}{x}}{2 + \frac{1}{x}}

= x \to \infty lim (\frac{3 + \frac{1}{x}}{2 + \frac{1}{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} ( 3 + \frac{1}{x} )}{lim _{x \to \infty} ( 2 + \frac{1}{x} )}

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

x \to \infty lim (2 + \frac{1}{x}) = 2

= \frac{3}{2}

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

x \to \infty lim (5 x + 3)

x \to 3 lim (\frac{4}{x - 1})

x \to \infty lim (\frac{3 x ^{2} - 7 x}{5 x ^{2} + 7})

x \to 5 - lim (\frac{sin ( ( x - 7 ) ( x - 5 ) )}{x - 5})

What is the limit as x approaches infinity of (3x+1)/(2x+1) ?
The limit as x approaches infinity of (3x+1)/(2x+1) is 3/2