What is the limit as x approaches infinity of (cos(1/x))^{1/(x^2)} ?

The limit as x approaches infinity of (cos(1/x))^{1/(x^2)} is 1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as x approaches infinity of (cos(1/x))^{1/(x^2)}

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

1

Solution steps

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

Apply exponent rules

= x \to \infty lim (e^{\frac{1}{x ^{2}} l n (c o s (\frac{1}{x}))})

Apply the Limit Chain Rule:

1

= 1

n = 3 \sum \infty \frac{n x ^{n}}{n + 2}

\frac{d x}{d t} - x = 5 t

\frac{\partial}{\partial x} (1 + ln (x y))

y^{^{''}} - 8 y^{^{'}} + 16 y = t^{- 2} e^{4 t}

x y^{2} y^{^{'}} = y^{3} - 3 x^{3}

What is the limit as x approaches infinity of (cos(1/x))^{1/(x^2)} ?
The limit as x approaches infinity of (cos(1/x))^{1/(x^2)} is 1