What is the limit as n approaches infinity of (1+sin(1/n))^{sqrt(n)} ?

The limit as n approaches infinity of (1+sin(1/n))^{sqrt(n)} is 1

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limit as n approaches infinity of (1+sin(1/n))^{sqrt(n)}

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

1

Solution steps

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

Apply exponent rules

= n \to \infty lim (e^{n l n (1 + s i n (\frac{1}{n}))})

Apply the Limit Chain Rule:

1

= 1

f (x) = x^{2} - 8 x - 91

f (x) = \frac{1}{x + 1}, at x = 0

\int 2 cos (x) sin^{2} (x) d x

x + 1

\frac{4 s + 7}{s ^{2} - 4}

What is the limit as n approaches infinity of (1+sin(1/n))^{sqrt(n)} ?
The limit as n approaches infinity of (1+sin(1/n))^{sqrt(n)} is 1