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

The limit as x approaches 0 of ((1+x)^6-1)/x is 6

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+x)^6-1)/x

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

6

Solution steps

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

Simplify

\frac{( 1 + x ) ^{6} - 1}{x} : (x + 2) ((x + 1)^{4} + (x + 1)^{2} + 1)

= x \to 0 lim ((x + 2) ((x + 1)^{4} + (x + 1)^{2} + 1))

Plug in the value

x = 0

= (0 + 2) ((0 + 1)^{4} + (0 + 1)^{2} + 1)

Simplify

(0 + 2) ((0 + 1)^{4} + (0 + 1)^{2} + 1) : 6

= 6

x y^{^{'}} - y = x^{2} e^{x}

\frac{\partial}{\partial x} (- 5 x y^{4} - 2 y cos (x))

cos (x)

\frac{d}{d x} (x^{2} \cdot 3 y)

\int 4 r^{2} + 1 d r

What is the limit as x approaches 0 of ((1+x)^6-1)/x ?
The limit as x approaches 0 of ((1+x)^6-1)/x is 6