What is the limit as h approaches 0 of (1+4h)^{1/h} ?

The limit as h approaches 0 of (1+4h)^{1/h} is e^4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as h approaches 0 of (1+4h)^{1/h}

h \to 0 lim ((1 + 4 h)^{\frac{1}{h}})

e^{4}

Decimal Notation

54.59815 \dots

Solution steps

h \to 0 lim ((1 + 4 h)^{\frac{1}{h}})

Apply exponent rules

= h \to 0 lim (e^{\frac{1}{h} l n (1 + 4 h)})

Apply the Limit Chain Rule:

e^{4}

= e^{4}

x \to 3 lim (\frac{e ^{x} - 1}{x})

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

x \to \infty lim ((x)^{0})

x \to 0 - lim (csch (x))

x \to 0 - lim (ln (1 + x))

What is the limit as h approaches 0 of (1+4h)^{1/h} ?
The limit as h approaches 0 of (1+4h)^{1/h} is e^4