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

The limit as x approaches 0 of ((1+x)^4-1)/x is 4

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)^4-1)/x

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

4

Solution steps

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

Simplify

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

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

Plug in the value

x = 0

= (0^{2} + 2 \cdot 0 + 2) (0 + 2)

Simplify

(0^{2} + 2 \cdot 0 + 2) (0 + 2) : 4

= 4

\frac{- 3 s + 9}{( s + 3 ) ^{2}}

\frac{d}{d t} (4 e^{t} sin (t))

\int (\frac{5}{x} - \frac{3}{x ^{2}}) d x

\int_{5}^{8} \frac{6}{x - 5} d x

t^{2} y^{^{'}} + y^{2} = t y, y (1) = - \frac{1}{2}

What is the limit as x approaches 0 of ((1+x)^4-1)/x ?
The limit as x approaches 0 of ((1+x)^4-1)/x is 4