What is the limit as x approaches infinity of (3x+1)/(sqrt(4x^2-3x-7)) ?

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limit as x approaches infinity of (3x+1)/(sqrt(4x^2-3x-7))

x \to \infty lim (\frac{3 x + 1}{4 x ^{2} - 3 x - 7})

\frac{3}{2}

Decimal Notation

1.5

Solution steps

x \to \infty lim (\frac{3 x + 1}{4 x ^{2} - 3 x - 7})

Divide by highest denominator power:

\frac{3 + \frac{1}{x}}{4 - \frac{3}{x} - \frac{7}{x ^{2}}}

= x \to \infty lim \frac{3 + \frac{1}{x}}{4 - \frac{3}{x} - \frac{7}{x ^{2}}}

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} ( 4 - \frac{3}{x} - \frac{7}{x ^{2}} )}

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

x \to \infty lim (4 - \frac{3}{x} - \frac{7}{x ^{2}}) = 2

= \frac{3}{2}

x \to 2 lim (x^{2} + x + 3)

x \to 4 lim (x^{2} + 3 x - 4)

x \to 0 lim (4 x^{7 x})

x \to 0 lim (ln (x^{x}))

x \to - \infty lim (x, 4)

What is the limit as x approaches infinity of (3x+1)/(sqrt(4x^2-3x-7)) ?
The limit as x approaches infinity of (3x+1)/(sqrt(4x^2-3x-7)) is 3/2