What is the limit as x approaches 0 of ((x+1)^5-1)/x ?

The limit as x approaches 0 of ((x+1)^5-1)/x is 5

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 ((x+1)^5-1)/x

x \to 0 lim (\frac{( x + 1 ) ^{5} - 1}{x})

5

Solution steps

x \to 0 lim (\frac{( x + 1 ) ^{5} - 1}{x})

Simplify

\frac{( x + 1 ) ^{5} - 1}{x} : x + (x + 1)^{4} + (x + 1)^{3} + (x + 1)^{2} + 2

= x \to 0 lim (x + (x + 1)^{4} + (x + 1)^{3} + (x + 1)^{2} + 2)

Plug in the value

x = 0

= 0 + (0 + 1)^{4} + (0 + 1)^{3} + (0 + 1)^{2} + 2

Simplify

0 + (0 + 1)^{4} + (0 + 1)^{3} + (0 + 1)^{2} + 2 : 5

= 5

\int A \cdot e^{t (1 + 3)} d t

\int \frac{1}{( u - 1 ) ^{2}} d u

\int - 8 x sin (4 x^{2} + 1) d x

x^{2} + 5 y \frac{d y}{d x} = 0

x \to - 1 lim ((9 x + 1)^{2})

What is the limit as x approaches 0 of ((x+1)^5-1)/x ?
The limit as x approaches 0 of ((x+1)^5-1)/x is 5