What is the limit as n approaches infinity of Arg(-1+i/n) ?

The limit as n approaches infinity of Arg(-1+i/n) is -Arg

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limit as n approaches infinity of Arg(-1+i/n)

n \to \infty lim (A r g (- 1 + \frac{i}{n}))

- A r g

Solution steps

n \to \infty lim (A r g (- 1 + \frac{i}{n}))

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= A r g \cdot n \to \infty lim (- 1 + \frac{i}{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

= A r g (- n \to \infty lim (1) + n \to \infty lim (\frac{i}{n}))

n \to \infty lim (1) = 1

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

= A r g (- 1 + 0)

Simplify

= - A r g

What is the limit as n approaches infinity of Arg(-1+i/n) ?
The limit as n approaches infinity of Arg(-1+i/n) is -Arg