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

The limit as x approaches 0 of (1-2x)^{2/x} is 1/(e^4)

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

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

\frac{1}{e ^{4}}

Decimal Notation

0.01831 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

\frac{1}{e ^{4}}

= \frac{1}{e ^{4}}

\int \frac{4 x ^{2} - 21 x}{( x - 3 ) ^{2} ( 2 x + 3 )} d x

\int \frac{ln ( x ) - 1}{x ^{2}} d x

\frac{1}{y ^{4}}

\int 40

\frac{d}{d x} (tan (x + \frac{π}{4}))

What is the limit as x approaches 0 of (1-2x)^{2/x} ?
The limit as x approaches 0 of (1-2x)^{2/x} is 1/(e^4)