What is the limit as n approaches infinity of 1+x/n ?

The limit as n approaches infinity of 1+x/n is 1

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limit as n approaches infinity of 1+x/n

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

1

Solution steps

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

n \to \infty lim (1) = 1

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

= 1 + 0

Simplify

= 1

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

x \to 0 - lim (\frac{3 x ^{2} + 2 x}{x})

x \to 0 + lim ((1 + 3 x)^{\frac{2}{x}})

x \to 0 lim (\frac{x + 5}{x - 3})

b \to 0 lim (cot (b) - csc (b))

What is the limit as n approaches infinity of 1+x/n ?
The limit as n approaches infinity of 1+x/n is 1