What is the limit as x approaches 0 of (1+4x)^{6/x} ?

The limit as x approaches 0 of (1+4x)^{6/x} is e^{24}

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+4x)^{6/x}

x \to 0 lim ((1 + 4 x)^{\frac{6}{x}})

e^{24}

Decimal

26489122129.843437

Solution steps

x \to 0 lim ((1 + 4 x)^{\frac{6}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{6}{x} l n (1 + 4 x)})

Apply the Limit Chain Rule:

e^{24}

= e^{24}

\frac{\partial}{\partial y} (3 x^{2} y + 5 x y^{3})

\frac{( 3 - x )}{4 x}

\int cos^{4} (3 - x) sin (3 - x) d x

y = x, y = 1 - x^{2}, - 1, 2

- \frac{39}{( 8 x + 5 ) ^{2}}, at x = 2

What is the limit as x approaches 0 of (1+4x)^{6/x} ?
The limit as x approaches 0 of (1+4x)^{6/x} is e^{24}