What is the limit as x approaches infinity of (5x+7)/(6x^2+3x-2) ?

The limit as x approaches infinity of (5x+7)/(6x^2+3x-2) is 0

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limit as x approaches infinity of (5x+7)/(6x^2+3x-2)

x \to \infty lim (\frac{5 x + 7}{6 x ^{2} + 3 x - 2})

0

Solution steps

x \to \infty lim (\frac{5 x + 7}{6 x ^{2} + 3 x - 2})

Divide by highest denominator power:

\frac{\frac{5}{x} + \frac{7}{x ^{2}}}{6 + \frac{3}{x} - \frac{2}{x ^{2}}}

= x \to \infty lim (\frac{\frac{5}{x} + \frac{7}{x ^{2}}}{6 + \frac{3}{x} - \frac{2}{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} ( \frac{5}{x} + \frac{7}{x ^{2}} )}{lim _{x \to \infty} ( 6 + \frac{3}{x} - \frac{2}{x ^{2}} )}

x \to \infty lim (\frac{5}{x} + \frac{7}{x ^{2}}) = 0

x \to \infty lim (6 + \frac{3}{x} - \frac{2}{x ^{2}}) = 6

= \frac{0}{6}

Apply rule

\frac{0}{a} = 0, a \neq = 0

= 0

k \to \infty lim ((1 - \frac{1}{2 k})^{k})

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

x \to 0 lim (\frac{x + 6}{x ^{2}})

s \to 1 + lim (\frac{in s}{s - 1})

x \to 0 - lim (x^{2} - \frac{5}{x})

What is the limit as x approaches infinity of (5x+7)/(6x^2+3x-2) ?
The limit as x approaches infinity of (5x+7)/(6x^2+3x-2) is 0