What is the limit as x approaches 0 of (cos(2x))^{1/(x^2)} ?

The limit as x approaches 0 of (cos(2x))^{1/(x^2)} is 1/(e^2)

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 (cos(2x))^{1/(x^2)}

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

\frac{1}{e ^{2}}

Decimal

0.13533 \dots

Solution steps

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

Apply exponent rules

= x \to 0 lim (e^{\frac{1}{x ^{2}} l n (c o s (2 x))})

Apply the Limit Chain Rule:

\frac{1}{e ^{2}}

= \frac{1}{e ^{2}}

\int 24 x^{2} + 2 x + 10 d x

n = 1 \sum \infty (- 2)^{n}

\frac{( s + 2 )}{s ^{2} + 7 s + 12}

\frac{\partial}{\partial x} (sin (3 x + 2 y + z))

y^{^{''}} - 2 \cdot y = 981, y^{^{'}} (0) = 0, y (0) = 0

What is the limit as x approaches 0 of (cos(2x))^{1/(x^2)} ?
The limit as x approaches 0 of (cos(2x))^{1/(x^2)} is 1/(e^2)