What is the limit as x approaches 0 of (e^x+x)^{4/x} ?

The limit as x approaches 0 of (e^x+x)^{4/x} is e^8

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 (e^x+x)^{4/x}

x \to 0 lim ((e^{x} + x)^{\frac{4}{x}})

e^{8}

Decimal Notation

2980.95798 \dots

Solution steps

x \to 0 lim ((e^{x} + x)^{\frac{4}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{4}{x} l n (e^{x} + x)})

Apply the Limit Chain Rule:

e^{8}

= e^{8}

\int 1 + x^{2} d x

n = 1 \sum \infty \frac{1}{( n ( n + 8 ) )}

\frac{d}{d x} (e^{- 6 x^{5}})

f (x) = x^{2} - 7

\int \frac{5}{( x + 1 ) ( x ^{2} + 4 )} d x

What is the limit as x approaches 0 of (e^x+x)^{4/x} ?
The limit as x approaches 0 of (e^x+x)^{4/x} is e^8