What is the limit as n approaches infinity of n/(sqrt(10+n)) ?

The limit as n approaches infinity of n/(sqrt(10+n)) is infinity

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limit as n approaches infinity of n/(sqrt(10+n))

n \to \infty lim (\frac{n}{10 + n})

\infty

Solution steps

n \to \infty lim (\frac{n}{10 + n})

Rationalize denominator

\frac{n}{10 + n} : \frac{n 10 + n}{10 + n}

= n \to \infty lim (\frac{n 10 + n}{10 + n})

Divide by highest denominator power:

\frac{10 + n}{\frac{10}{n} + 1}

= n \to \infty lim (\frac{10 + n}{\frac{10}{n} + 1})

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 _{n \to \infty} ( 10 + n )}{lim _{n \to \infty} ( \frac{10}{n} + 1 )}

n \to \infty lim (10 + n) = \infty

n \to \infty lim (\frac{10}{n} + 1) = 1

= \frac{\infty}{1}

Apply Infinity Property:

\frac{\infty}{c} = \infty

= \infty

in v erse l a pl a ce \frac{( s + 2 ) ^{2}}{s ^{3}}

x \to 3 lim (\frac{x - 3}{x ^{2} + 9})

\int \frac{x + 5}{x ^{2} + 4 x + 3} d x

x \to - 8 lim (x + 6)

\frac{d y}{d x} - 2 x y = 10, y (0) = - 8

What is the limit as n approaches infinity of n/(sqrt(10+n)) ?
The limit as n approaches infinity of n/(sqrt(10+n)) is infinity