What is the limit as y approaches infinity of (sqrt(y^2+2))/(5y-6) ?

The limit as y approaches infinity of (sqrt(y^2+2))/(5y-6) is 1/5

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limit as y approaches infinity of (sqrt(y^2+2))/(5y-6)

y \to \infty lim (\frac{y ^{2} + 2}{5 y - 6})

\frac{1}{5}

Decimal

0.2

Solution steps

y \to \infty lim (\frac{y ^{2} + 2}{5 y - 6})

Divide by highest denominator power:

\frac{1 + \frac{2}{y ^{2}}}{5 - \frac{6}{y}}

= y \to \infty lim \frac{1 + \frac{2}{y ^{2}}}{5 - \frac{6}{y}}

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 _{y \to \infty} ( 1 + \frac{2}{y ^{2}} )}{lim _{y \to \infty} ( 5 - \frac{6}{y} )}

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

y \to \infty lim (5 - \frac{6}{y}) = 5

= \frac{1}{5}

What is the limit as y approaches infinity of (sqrt(y^2+2))/(5y-6) ?
The limit as y approaches infinity of (sqrt(y^2+2))/(5y-6) is 1/5