What is the limit as n approaches infinity of x+x/n ?

The limit as n approaches infinity of x+x/n is x

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limit as n approaches infinity of x+x/n

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

x

Solution steps

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

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

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

n \to \infty lim (x) = x

n \to \infty lim (\frac{x}{n}) = 0

= x + 0

Simplify

= x

\int (x^{2} - 2 x + 5) e^{x} d x

\int cos (- 2 x) d x

\frac{d x}{d t} + x = 3 e^{t}

y^{^{'}} - y = e^{3 x}

f (x) = 11 x^{4} cot (x)

What is the limit as n approaches infinity of x+x/n ?
The limit as n approaches infinity of x+x/n is x