What is the limit as x approaches 0 of (e^x+x)^{7/x} ?

The limit as x approaches 0 of (e^x+x)^{7/x} is e^{14}

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)^{7/x}

x \to 0 lim ((e^{x} + x)^{\frac{7}{x}})

e^{14}

Decimal Notation

1202604.28416 \dots

Solution steps

x \to 0 lim ((e^{x} + x)^{\frac{7}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{7}{x} l n (e^{x} + x)})

Apply the Limit Chain Rule:

e^{14}

= e^{14}

x \to 3 lim (\frac{x ^{2} - 6 x - 9}{x - 3})

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

x \to 0 lim (\frac{3 x}{e ^{4 x}})

x \to 0 lim (- \frac{∣ x ∣}{x})

x \to 1 lim (x^{3} - x^{2} - x + 1)

What is the limit as x approaches 0 of (e^x+x)^{7/x} ?
The limit as x approaches 0 of (e^x+x)^{7/x} is e^{14}