What is the limit as x approaches 0 of (2-cos(x))^{csc^2(x)} ?

The limit as x approaches 0 of (2-cos(x))^{csc^2(x)} is sqrt(e)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as x approaches 0 of (2-cos(x))^{csc^2(x)}

x \to 0 lim ((2 - cos (x))^{c s c^{2} (x)})

e

Decimal Notation

1.64872 \dots

Solution steps

x \to 0 lim ((2 - cos (x))^{c s c^{2} (x)})

Apply exponent rules

= x \to 0 lim (e^{c s c^{2} (x) l n (2 - c o s (x))})

Apply the Limit Chain Rule:

e

= e

x \to 4 lim (\frac{3}{5} x + 5)

x \to \frac{1}{8} lim (\frac{1}{2} + x^{- 1})

x \to 0 lim (ln (sin^{2} (x)))

x \to \infty lim (\frac{2}{6 x})

x \to 1 + lim (\frac{3}{x - 1})

What is the limit as x approaches 0 of (2-cos(x))^{csc^2(x)} ?
The limit as x approaches 0 of (2-cos(x))^{csc^2(x)} is sqrt(e)