What is the limit as x approaches 0 of (1+sin(3x))^{1/x} ?

The limit as x approaches 0 of (1+sin(3x))^{1/x} is e^3

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 (1+sin(3x))^{1/x}

x \to 0 lim ((1 + sin (3 x))^{\frac{1}{x}})

e^{3}

Decimal Notation

20.08553 \dots

Solution steps

x \to 0 lim ((1 + sin (3 x))^{\frac{1}{x}})

x \to a - lim f (x) = x \to a + lim f (x) = L

then

x \to a lim f (x) = L

x \to 0 - lim ((1 + sin (3 x))^{\frac{1}{x}}) = e^{3}

x \to 0 + lim ((1 + sin (3 x))^{\frac{1}{x}}) = e^{3}

= e^{3}

\frac{d}{d x} (\frac{π x ^{2}}{2})

\frac{d}{d x} ((1 + sin (x)) cos (x))

\frac{\partial}{\partial y} (3 x^{2} - 3)

\int \frac{7 x ^{6} + 6}{x ^{7} + 6 x} d x

\int e^{10 x} - 9 d x

What is the limit as x approaches 0 of (1+sin(3x))^{1/x} ?
The limit as x approaches 0 of (1+sin(3x))^{1/x} is e^3